<PAGE>   1
 
     AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON JUNE 19, 1998
 
                                           REGISTRATION STATEMENT NO. 333-
POST-EFFECTIVE AMENDMENT NO. 1 TO REGISTRATION STATEMENT NO. 333-07875
================================================================================
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549
                            ------------------------
 
                                    FORM S-8
                             REGISTRATION STATEMENT
                          AND POST-EFFECTIVE AMENDMENT
                                     UNDER
                           THE SECURITIES ACT OF 1933
                            ------------------------
 
                         LEHMAN BROTHERS HOLDINGS INC.
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)
 
<TABLE>
<S>                                        <C>
                 DELAWARE                                  13-3216325
     (STATE OR OTHER JURISDICTION OF                    (I.R.S. EMPLOYER
      INCORPORATION OR ORGANIZATION)                 IDENTIFICATION NUMBER)
 
         3 WORLD FINANCIAL CENTER                            10285
            NEW YORK, NEW YORK                             (ZIP CODE)
 (ADDRESS OF PRINCIPAL EXECUTIVE OFFICES)
</TABLE>
 
             LEHMAN BROTHERS HOLDINGS INC. EMPLOYEE INCENTIVE PLAN
          LEHMAN BROTHERS HOLDINGS INC. 1996 MANAGEMENT OWNERSHIP PLAN
                           (FULL TITLE OF THE PLANS)
                            ------------------------
 
                             THOMAS A. RUSSO, ESQ.
                            3 WORLD FINANCIAL CENTER
                            NEW YORK, NEW YORK 10285
                    (NAME AND ADDRESS OF AGENT FOR SERVICE)
 
                                 (212) 526-7000
         (TELEPHONE NUMBER, INCLUDING AREA CODE, OF AGENT FOR SERVICE)
                            ------------------------
 
                                    COPY TO:
 
                              JENNIFER MARRE, ESQ.
                         LEHMAN BROTHERS HOLDINGS INC.
                            3 WORLD FINANCIAL CENTER
                            NEW YORK, NEW YORK 10285
                            ------------------------
 
                        CALCULATION OF REGISTRATION FEE
 
<TABLE>
<S>                                <C>                 <C>                 <C>                 <C>
==================================================================================================================
                                                            PROPOSED            PROPOSED
                                                             MAXIMUM             MAXIMUM            AMOUNT OF
TITLE OF SECURITIES TO                AMOUNT TO BE       OFFERING PRICE         AGGREGATE         REGISTRATION
BE REGISTERED                         REGISTERED(1)       PER SHARE(2)      OFFERING PRICE(2)       FEE(1)(2)
------------------------------------------------------------------------------------------------------------------
Common Stock, $.10 par value per
  share(3)........................     10,000,000           $72.1875          $721,875,000         $212,953.13
------------------------------------------------------------------------------------------------------------------
Common Stock, $.10 par value per
  share(4)........................      5,500,000           $72.1875          $397,031,250         $117,124.22
==================================================================================================================
</TABLE>
 
(1) An aggregate of 30,000,000 shares of Common Stock were previously registered
    pursuant to the Registrant's Form S-8 Registration Statement, No. 333-07875,
    with respect to the plans identified above (the "Plans"). On or about July
    10, 1996, the Registrant paid an aggregate filing fee of $242,482.76 in
    connection with such Registration Statement, which was declared effective on
    July 29, 1996. Of those shares, 29,099,031 have not yet been issued under
    the Plans and are being carried forward to this Registration Statement in
    accordance with Rule 429 under the Securities Act of 1933. This Form S-8
    Registration Statement is being filed to register an additional aggregate of
    15,500,000 shares of Common Stock issuable under the Plans (and to file
    updated versions of the Plans as exhibits hereto).
 
(2) Pursuant to Rule 457(h) under the Securities Act of 1933, the proposed
    maximum offering price per share, the proposed maximum aggregate offering
    price and the amount of registration fee have been computed on the basis of
    the average of the high and low prices per share of Common Stock on the New
    York Stock Exchange on June 16, 1998.
 
(3) Represents Common Stock issuable under the Employee Incentive Plan.
 
(4) Represents Common Stock issuable under the 1996 Management Ownership Plan.
                            ------------------------
 
     PURSUANT TO RULE 429 UNDER THE SECURITIES ACT OF 1933, THE PROSPECTUS
PREPARED IN CONNECTION HEREWITH IS A COMBINED PROSPECTUS ALSO RELATING TO UNSOLD
SHARES OF COMMON STOCK COVERED BY REGISTRATION STATEMENT NO. 333-07875
PREVIOUSLY FILED WITH THE COMMISSION ON FORM S-8 AND DECLARED EFFECTIVE JULY 29,
1996. THIS REGISTRATION STATEMENT ALSO CONSTITUTES POST-EFFECTIVE AMENDMENT NO.
1 TO REGISTRATION STATEMENT NO. 333-07875.
================================================================================
<PAGE>   2
 
                                    PART II
 
               INFORMATION REQUIRED IN THE REGISTRATION STATEMENT
 
ITEM 3.  INCORPORATION OF DOCUMENTS BY REFERENCE
 
     The following documents previously filed by Lehman Brothers Holdings Inc.
(the "Registrant") with the Securities and Exchange Commission (the "SEC")
pursuant to the Securities Exchange Act of 1934 (the "Exchange Act") are hereby
incorporated by reference in this Registration Statement:
 
     (1) The Registrant's Annual Report on Form 10-K for the fiscal year ended
         November 30, 1997, filed with the SEC on February 27, 1998;
 
     (2) The Registrant's Quarterly Report on Form 10-Q for the quarterly period
         ended February 28, 1998, filed with the SEC on April 14, 1998;
 
     (3) The Registrant's Current Reports on Form 8-K, filed with the SEC on
         January 7, 1998, March 25, 1998, April 6, 1998, May 13, 1998 and June
         18, 1998; and
 
     (4) The description of the Registrant's Common Stock, as contained in the
         Registrant's Form 8-A Registration Statement, filed with the SEC on
         April 29, 1994.
 
     Each document filed by the Registrant pursuant to Section 13(a), 13(c), 14
or 15(d) of the Exchange Act after the date of this Registration Statement and
prior to the filing of a post-effective amendment to this Registration Statement
indicating that all securities offered have been sold or which deregisters all
securities then remaining unsold shall be deemed to be incorporated by reference
into this Registration Statement from the date of filing of such document. Any
statement contained in a document incorporated or deemed to be incorporated by
reference herein shall be deemed to be modified or superseded for purposes of
this Registration Statement to the extent that a statement contained herein or
in any subsequently filed document which also is or is deemed to be incorporated
by reference herein modifies or supersedes such statement. Any such statement so
modified or superseded shall not be deemed, except as so modified or superseded,
to constitute a part of this Registration Statement.
 
ITEM 4.  DESCRIPTION OF SECURITIES
 
     Not applicable.
 
ITEM 5.  INTERESTS OF NAMED EXPERTS AND COUNSEL
 
     Karen M. Muller, Managing Director of Lehman Brothers Inc., the
Registrant's wholly-owned subsidiary, and a Vice President and Deputy General
Counsel of the Registrant, has rendered an opinion to the effect that, under
applicable state law, the shares of Common Stock to which this Registration
Statement relates will be, when issued, validly issued, fully paid and
nonassessable.
 
ITEM 6.  INDEMNIFICATION OF DIRECTORS AND OFFICERS
 
     The Restated Certificate of Incorporation of the Registrant requires the
Registrant to indemnify its directors and officers to the fullest extent
permitted by Delaware General Corporation Law. In addition, the officers and
directors of the Registrant are insured under officers' and directors' liability
insurance policies purchased by the Registrant. The directors, officers and
employees of the Registrant are also insured against fiduciary liabilities under
the Employee Retirement Income Security Act of 1974.
 
ITEM 7.  EXEMPTION FROM REGISTRATION CLAIMED
 
     Not applicable.
 
ITEM 8.  EXHIBITS
 
     The Exhibit Index beginning on page E-1 is hereby incorporated by
reference.
 
                                      II-1
<PAGE>   3
 
ITEM 9.  UNDERTAKINGS
 
     (a) The undersigned Registrant hereby undertakes:
 
          (1) To file, during any period in which offers or sales are being
     made, a post-effective amendment to this Registration Statement:
 
             (i) To include any prospectus required by Section 10(a)(3) of the
        Securities Act of 1933 (the "Securities Act");
 
             (ii) To reflect in the prospectus any facts or events arising after
        the effective date of this Registration Statement (or the most recent
        post-effective amendment thereof) which, individually or in the
        aggregate, represent a fundamental change in the information set forth
        in this Registration Statement. Notwithstanding the foregoing, any
        increase or decrease in volume of securities offered (if the total
        dollar value of securities offered would not exceed that which was
        registered) and any deviation from the low or high end of the estimated
        maximum offering range may be reflected in the form of prospectus filed
        with the Commission pursuant to Rule 424(b) if, in the aggregate, the
        changes in volume and price represent no more than a 20 percent change
        in the maximum aggregate offering price set forth in the "Calculation of
        Registration Fee" table in the effective registration statement; and
 
             (iii) To include any material information with respect to the plan
        of distribution not previously disclosed in this Registration Statement
        or any material change to such information in this Registration
        Statement;
 
     provided, however, that the undertakings set forth in paragraphs (i) and
     (ii) above do not apply if this Registration Statement is on Form S-3, Form
     S-8 or Form F-3, and the information required to be included in a
     post-effective amendment by those paragraphs is contained in periodic
     reports filed with or furnished to the SEC by the Registrant pursuant to
     Section 13 or 15(d) of the Exchange Act that are incorporated by reference
     in this Registration Statement.
 
          (2) That, for the purpose of determining any liability under the
     Securities Act, each such post-effective amendment shall be deemed to be a
     new registration statement relating to the securities offered therein, and
     the offering of such securities at that time shall be deemed to be the
     initial bona fide offering thereof.
 
          (3) To remove from registration by means of a post-effective amendment
     any of the securities being registered which remain unsold at the
     termination of the offering.
 
     (b) The undersigned Registrant hereby undertakes that, for purposes of
determining any liability under the Securities Act, each filing of the
Registrant's annual report pursuant to Section 13(a) or 15(d) of the Exchange
Act (and, where applicable, each filing of an employee benefit plan's annual
report pursuant to Section 15(d) of the Exchange Act) that is incorporated by
reference in this Registration Statement shall be deemed to be a new
registration statement relating to the securities offered therein, and the
offering of such securities at that time shall be deemed to be the initial bona
fide offering thereof.
 
     (c) Insofar as indemnification for liabilities arising under the Securities
Act may be permitted to directors, officers and controlling persons of the
Registrant pursuant to the foregoing provisions, or otherwise, the Registrant
has been advised that in the opinion of the SEC such indemnification is against
public policy as expressed in the Securities Act and is, therefore,
unenforceable. In the event that a claim for indemnification against such
liabilities (other than the payment by the Registrant of expenses incurred or
paid by a director, officer or controlling person of the Registrant in the
successful defense of any action, suit or proceeding) is asserted by such
director, officer or controlling person in connection with the securities being
registered, the Registrant will, unless in the opinion of its counsel the matter
has been settled by controlling precedent, submit to a court of appropriate
jurisdiction the question whether such indemnification by it is against public
policy as expressed in the Securities Act and will be governed by the final
adjudication of such issue.
 
                                      II-2
<PAGE>   4
 
                                   SIGNATURES
 
     Pursuant to the requirements of the Securities Act of 1933, the Registrant
certifies that it has reasonable grounds to believe that it meets all of the
requirements for filing on Form S-8 and has duly caused this Registration
Statement to be signed on its behalf by the undersigned, thereunto duly
authorized, in the City of New York, State of New York, on June 19, 1998.
 
                                         LEHMAN BROTHERS HOLDINGS INC.
 
                                          By:         /s/ KAREN M. MULLER
 
                                            ------------------------------------
                                                      Karen M. Muller
                                                       Vice President
 
                                      II-3
<PAGE>   5
 
     Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed below by the following persons in the
capacities indicated.
 
Dated: June 19, 1998
 
<TABLE>
<CAPTION>
                     SIGNATURE                                      TITLE
                     ---------                                      -----
<C>                                                  <S>                                  <C>
 
                         *                           Chief Executive Officer and
---------------------------------------------------    Chairman of the Board of
               Richard S. Fuld, Jr.                    Directors
                                                       (principal executive officer)
 
                         *                           Chief Financial Officer
---------------------------------------------------    (principal financial and
                 Charles B. Hintz                      accounting officer)
 
                         *                           Director
---------------------------------------------------
                Michael L. Ainslie
 
                         *                           Director
---------------------------------------------------
                   John F. Akers
 
                         *                           Director
---------------------------------------------------
                 Roger S. Berlind
 
                         *                           Director
---------------------------------------------------
               Thomas H. Cruikshank
 
                         *                           Director
---------------------------------------------------
                   Henry Kaufman
 
                         *                           Director
---------------------------------------------------
               Hideichiro Kobayashi
 
                         *                           Director
---------------------------------------------------
                 John D. Macomber
 
                                                     Director
---------------------------------------------------
                   Dina Merrill
 
         *By          /s/ KAREN M. MULLER
  ----------------------------------------------
                  Karen M. Muller
                 Attorney-in-Fact
</TABLE>
 
                                      II-4
<PAGE>   6
 
                                 EXHIBIT INDEX
 
<TABLE>
<CAPTION>
EXHIBIT                                                              FILED HEREWITH (--) OR
NUMBER                         DESCRIPTION                        INCORPORATED BY REFERENCE TO
-------                        -----------                        ----------------------------
<C>        <S>                                                   <C>
 
   4.1     Restated Certificate of Incorporation of the          Exhibit 3.1 of the
           Registrant dated May 27, 1994                         Registrant's Transition Report
                                                                 on Form 10-K for the eleven
                                                                 months ended November 30,
                                                                 1994, filed with the SEC on
                                                                 February 28, 1995
 
   4.2     Certificate of Designations with respect to the       Exhibit 4.1 of the
           Registrant's Series C Preferred Stock                 Registrant's Current Report on
                                                                 Form 8-K, filed with the SEC
                                                                 on May 13, 1998
 
   4.3     By-Laws of the Registrant, amended as of March 26,    Exhibit 3 of the Registrant's
           1997                                                  Quarterly Report on Form 10-Q
                                                                 for the quarterly period ended
                                                                 February 28, 1997, filed with
                                                                 the SEC on April 14, 1997
 
   4.4     Employee Incentive Plan                                             --
 
   4.5     1996 Management Ownership Plan                                      --
 
   5.1     Opinion (and consent) of Karen M. Muller as to the                  --
           validity of the shares of Common Stock to which this
           Registration Statement relates
 
  23.1     Consent of Karen M. Muller (included in Exhibit 5.1)                --
 
  23.2     Consent of Ernst & Young LLP, Independent Auditors                  --
 
  24.1     Power of Attorney                                                   --
</TABLE>
 
                                       E-1
[{"type": "S-8", "sequence": "1", "description": "FORM S-8 FOR LEHMAN BROTHERS HOLDINGS INC.", "secsgml_size_bytes": 19255}]
{"company-data": {"conformed-name": "LEHMAN BROTHERS HOLDINGS INC", "cik": "0000806085", "assigned-sic": "6211", "irs-number": "133216325", "state-of-incorporation": "DE", "fiscal-year-end": "1130"}, "filing-values": {"form-type": "S-8", "act": "33", "file-number": "333-57239", "film-number": "98650928"}, "business-address": {"street1": "AMERICAN EXPRESS TWR", "street2": "3 WORLD FINANCIAL CNTR", "city": "NEW YORK", "state": "NY", "zip": "10285", "phone": "2125267000"}, "mail-address": {"street1": "AMERICAN EXPRESS TOWER 15TH FL", "street2": "2 WORLD TRADE CENTER", "city": "NEW YORK", "state": "NY", "zip": "10048"}, "former-company": {"former-conformed-name": "SHEARSON LEHMAN HUTTON HOLDINGS INC", "date-changed": "19901017"}}
1
 
     AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON JUNE 19, 1998
 
                                           REGISTRATION STATEMENT NO. 333-
POST-EFFECTIVE AMENDMENT NO. 1 TO REGISTRATION STATEMENT NO. 333-07875
================================================================================
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549
                            ------------------------
 
                                    FORM S-8
                             REGISTRATION STATEMENT
                          AND POST-EFFECTIVE AMENDMENT
                                     UNDER
                           THE SECURITIES ACT OF 1933
                            ------------------------
 
                         LEHMAN BROTHERS HOLDINGS INC.
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)
DELAWARE                                  13-3216325
     (STATE OR OTHER JURISDICTION OF                    (I.R.S. EMPLOYER
      INCORPORATION OR ORGANIZATION)                 IDENTIFICATION NUMBER)
 
         3 WORLD FINANCIAL CENTER                            10285
            NEW YORK, NEW YORK                             (ZIP CODE)
 (ADDRESS OF PRINCIPAL EXECUTIVE OFFICES)
LEHMAN BROTHERS HOLDINGS INC. EMPLOYEE INCENTIVE PLAN
          LEHMAN BROTHERS HOLDINGS INC. 1996 MANAGEMENT OWNERSHIP PLAN
                           (FULL TITLE OF THE PLANS)
                            ------------------------
 
                             THOMAS A. RUSSO, ESQ.
                            3 WORLD FINANCIAL CENTER
                            NEW YORK, NEW YORK 10285
                    (NAME AND ADDRESS OF AGENT FOR SERVICE)
 
                                 (212) 526-7000
         (TELEPHONE NUMBER, INCLUDING AREA CODE, OF AGENT FOR SERVICE)
                            ------------------------
 
                                    COPY TO:
 
                              JENNIFER MARRE, ESQ.
                         LEHMAN BROTHERS HOLDINGS INC.
                            3 WORLD FINANCIAL CENTER
                            NEW YORK, NEW YORK 10285
                            ------------------------
 
                        CALCULATION OF REGISTRATION FEE
==================================================================================================================
                                                            PROPOSED            PROPOSED
                                                             MAXIMUM             MAXIMUM            AMOUNT OF
TITLE OF SECURITIES TO                AMOUNT TO BE       OFFERING PRICE         AGGREGATE         REGISTRATION
BE REGISTERED                         REGISTERED(1)       PER SHARE(2)      OFFERING PRICE(2)       FEE(1)(2)
------------------------------------------------------------------------------------------------------------------
Common Stock, $.10 par value per
  share(3)........................     10,000,000           $72.1875          $721,875,000         $212,953.13
------------------------------------------------------------------------------------------------------------------
Common Stock, $.10 par value per
  share(4)........................      5,500,000           $72.1875          $397,031,250         $117,124.22
==================================================================================================================
(1) An aggregate of 30,000,000 shares of Common Stock were previously registered
    pursuant to the Registrant's Form S-8 Registration Statement, No. 333-07875,
    with respect to the plans identified above (the "Plans"). On or about July
    10, 1996, the Registrant paid an aggregate filing fee of $242,482.76 in
    connection with such Registration Statement, which was declared effective on
    July 29, 1996. Of those shares, 29,099,031 have not yet been issued under
    the Plans and are being carried forward to this Registration Statement in
    accordance with Rule 429 under the Securities Act of 1933. This Form S-8
    Registration Statement is being filed to register an additional aggregate of
    15,500,000 shares of Common Stock issuable under the Plans (and to file
    updated versions of the Plans as exhibits hereto).
 
(2) Pursuant to Rule 457(h) under the Securities Act of 1933, the proposed
    maximum offering price per share, the proposed maximum aggregate offering
    price and the amount of registration fee have been computed on the basis of
    the average of the high and low prices per share of Common Stock on the New
    York Stock Exchange on June 16, 1998.
 
(3) Represents Common Stock issuable under the Employee Incentive Plan.
 
(4) Represents Common Stock issuable under the 1996 Management Ownership Plan.
                            ------------------------
 
     PURSUANT TO RULE 429 UNDER THE SECURITIES ACT OF 1933, THE PROSPECTUS
PREPARED IN CONNECTION HEREWITH IS A COMBINED PROSPECTUS ALSO RELATING TO UNSOLD
SHARES OF COMMON STOCK COVERED BY REGISTRATION STATEMENT NO. 333-07875
PREVIOUSLY FILED WITH THE COMMISSION ON FORM S-8 AND DECLARED EFFECTIVE JULY 29,
1996. THIS REGISTRATION STATEMENT ALSO CONSTITUTES POST-EFFECTIVE AMENDMENT NO.
1 TO REGISTRATION STATEMENT NO. 333-07875.
================================================================================
2
 
                                    PART II
 
               INFORMATION REQUIRED IN THE REGISTRATION STATEMENT
 
ITEM 3.  INCORPORATION OF DOCUMENTS BY REFERENCE
 
     The following documents previously filed by Lehman Brothers Holdings Inc.
(the "Registrant") with the Securities and Exchange Commission (the "SEC")
pursuant to the Securities Exchange Act of 1934 (the "Exchange Act") are hereby
incorporated by reference in this Registration Statement:
 
     (1) The Registrant's Annual Report on Form 10-K for the fiscal year ended
         November 30, 1997, filed with the SEC on February 27, 1998;
 
     (2) The Registrant's Quarterly Report on Form 10-Q for the quarterly period
         ended February 28, 1998, filed with the SEC on April 14, 1998;
 
     (3) The Registrant's Current Reports on Form 8-K, filed with the SEC on
         January 7, 1998, March 25, 1998, April 6, 1998, May 13, 1998 and June
         18, 1998; and
 
     (4) The description of the Registrant's Common Stock, as contained in the
         Registrant's Form 8-A Registration Statement, filed with the SEC on
         April 29, 1994.
 
     Each document filed by the Registrant pursuant to Section 13(a), 13(c), 14
or 15(d) of the Exchange Act after the date of this Registration Statement and
prior to the filing of a post-effective amendment to this Registration Statement
indicating that all securities offered have been sold or which deregisters all
securities then remaining unsold shall be deemed to be incorporated by reference
into this Registration Statement from the date of filing of such document. Any
statement contained in a document incorporated or deemed to be incorporated by
reference herein shall be deemed to be modified or superseded for purposes of
this Registration Statement to the extent that a statement contained herein or
in any subsequently filed document which also is or is deemed to be incorporated
by reference herein modifies or supersedes such statement. Any such statement so
modified or superseded shall not be deemed, except as so modified or superseded,
to constitute a part of this Registration Statement.
 
ITEM 4.  DESCRIPTION OF SECURITIES
 
     Not applicable.
 
ITEM 5.  INTERESTS OF NAMED EXPERTS AND COUNSEL
 
     Karen M. Muller, Managing Director of Lehman Brothers Inc., the
Registrant's wholly-owned subsidiary, and a Vice President and Deputy General
Counsel of the Registrant, has rendered an opinion to the effect that, under
applicable state law, the shares of Common Stock to which this Registration
Statement relates will be, when issued, validly issued, fully paid and
nonassessable.
 
ITEM 6.  INDEMNIFICATION OF DIRECTORS AND OFFICERS
 
     The Restated Certificate of Incorporation of the Registrant requires the
Registrant to indemnify its directors and officers to the fullest extent
permitted by Delaware General Corporation Law. In addition, the officers and
directors of the Registrant are insured under officers' and directors' liability
insurance policies purchased by the Registrant. The directors, officers and
employees of the Registrant are also insured against fiduciary liabilities under
the Employee Retirement Income Security Act of 1974.
 
ITEM 7.  EXEMPTION FROM REGISTRATION CLAIMED
 
     Not applicable.
 
ITEM 8.  EXHIBITS
 
     The Exhibit Index beginning on page E-1 is hereby incorporated by
reference.
 
                                      II-1
3
 
ITEM 9.  UNDERTAKINGS
 
     (a) The undersigned Registrant hereby undertakes:
 
          (1) To file, during any period in which offers or sales are being
     made, a post-effective amendment to this Registration Statement:
 
             (i) To include any prospectus required by Section 10(a)(3) of the
        Securities Act of 1933 (the "Securities Act");
 
             (ii) To reflect in the prospectus any facts or events arising after
        the effective date of this Registration Statement (or the most recent
        post-effective amendment thereof) which, individually or in the
        aggregate, represent a fundamental change in the information set forth
        in this Registration Statement. Notwithstanding the foregoing, any
        increase or decrease in volume of securities offered (if the total
        dollar value of securities offered would not exceed that which was
        registered) and any deviation from the low or high end of the estimated
        maximum offering range may be reflected in the form of prospectus filed
        with the Commission pursuant to Rule 424(b) if, in the aggregate, the
        changes in volume and price represent no more than a 20 percent change
        in the maximum aggregate offering price set forth in the "Calculation of
        Registration Fee" table in the effective registration statement; and
 
             (iii) To include any material information with respect to the plan
        of distribution not previously disclosed in this Registration Statement
        or any material change to such information in this Registration
        Statement;
 
     provided, however, that the undertakings set forth in paragraphs (i) and
     (ii) above do not apply if this Registration Statement is on Form S-3, Form
     S-8 or Form F-3, and the information required to be included in a
     post-effective amendment by those paragraphs is contained in periodic
     reports filed with or furnished to the SEC by the Registrant pursuant to
     Section 13 or 15(d) of the Exchange Act that are incorporated by reference
     in this Registration Statement.
 
          (2) That, for the purpose of determining any liability under the
     Securities Act, each such post-effective amendment shall be deemed to be a
     new registration statement relating to the securities offered therein, and
     the offering of such securities at that time shall be deemed to be the
     initial bona fide offering thereof.
 
          (3) To remove from registration by means of a post-effective amendment
     any of the securities being registered which remain unsold at the
     termination of the offering.
 
     (b) The undersigned Registrant hereby undertakes that, for purposes of
determining any liability under the Securities Act, each filing of the
Registrant's annual report pursuant to Section 13(a) or 15(d) of the Exchange
Act (and, where applicable, each filing of an employee benefit plan's annual
report pursuant to Section 15(d) of the Exchange Act) that is incorporated by
reference in this Registration Statement shall be deemed to be a new
registration statement relating to the securities offered therein, and the
offering of such securities at that time shall be deemed to be the initial bona
fide offering thereof.
 
     (c) Insofar as indemnification for liabilities arising under the Securities
Act may be permitted to directors, officers and controlling persons of the
Registrant pursuant to the foregoing provisions, or otherwise, the Registrant
has been advised that in the opinion of the SEC such indemnification is against
public policy as expressed in the Securities Act and is, therefore,
unenforceable. In the event that a claim for indemnification against such
liabilities (other than the payment by the Registrant of expenses incurred or
paid by a director, officer or controlling person of the Registrant in the
successful defense of any action, suit or proceeding) is asserted by such
director, officer or controlling person in connection with the securities being
registered, the Registrant will, unless in the opinion of its counsel the matter
has been settled by controlling precedent, submit to a court of appropriate
jurisdiction the question whether such indemnification by it is against public
policy as expressed in the Securities Act and will be governed by the final
adjudication of such issue.
 
                                      II-2
4
 
                                   SIGNATURES
 
     Pursuant to the requirements of the Securities Act of 1933, the Registrant
certifies that it has reasonable grounds to believe that it meets all of the
requirements for filing on Form S-8 and has duly caused this Registration
Statement to be signed on its behalf by the undersigned, thereunto duly
authorized, in the City of New York, State of New York, on June 19, 1998.
 
                                         LEHMAN BROTHERS HOLDINGS INC.
 
                                          By:         /s/ KAREN M. MULLER
 
                                            ------------------------------------
                                                      Karen M. Muller
                                                       Vice President
 
                                      II-3
5
 
     Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed below by the following persons in the
capacities indicated.
 
Dated: June 19, 1998
SIGNATURE                                      TITLE
                     ---------                                      -----
*                           Chief Executive Officer and
---------------------------------------------------    Chairman of the Board of
               Richard S. Fuld, Jr.                    Directors
                                                       (principal executive officer)
 
                         *                           Chief Financial Officer
---------------------------------------------------    (principal financial and
                 Charles B. Hintz                      accounting officer)
 
                         *                           Director
---------------------------------------------------
                Michael L. Ainslie
 
                         *                           Director
---------------------------------------------------
                   John F. Akers
 
                         *                           Director
---------------------------------------------------
                 Roger S. Berlind
 
                         *                           Director
---------------------------------------------------
               Thomas H. Cruikshank
 
                         *                           Director
---------------------------------------------------
                   Henry Kaufman
 
                         *                           Director
---------------------------------------------------
               Hideichiro Kobayashi
 
                         *                           Director
---------------------------------------------------
                 John D. Macomber
 
                                                     Director
---------------------------------------------------
                   Dina Merrill
 
         *By          /s/ KAREN M. MULLER
  ----------------------------------------------
                  Karen M. Muller
                 Attorney-in-Fact
II-4
6
 
                                 EXHIBIT INDEX
EXHIBIT                                                              FILED HEREWITH (--) OR
NUMBER                         DESCRIPTION                        INCORPORATED BY REFERENCE TO
-------                        -----------                        ----------------------------
4.1     Restated Certificate of Incorporation of the          Exhibit 3.1 of the
           Registrant dated May 27, 1994                         Registrant's Transition Report
                                                                 on Form 10-K for the eleven
                                                                 months ended November 30,
                                                                 1994, filed with the SEC on
                                                                 February 28, 1995
 
   4.2     Certificate of Designations with respect to the       Exhibit 4.1 of the
           Registrant's Series C Preferred Stock                 Registrant's Current Report on
                                                                 Form 8-K, filed with the SEC
                                                                 on May 13, 1998
 
   4.3     By-Laws of the Registrant, amended as of March 26,    Exhibit 3 of the Registrant's
           1997                                                  Quarterly Report on Form 10-Q
                                                                 for the quarterly period ended
                                                                 February 28, 1997, filed with
                                                                 the SEC on April 14, 1997
 
   4.4     Employee Incentive Plan                                             --
 
   4.5     1996 Management Ownership Plan                                      --
 
   5.1     Opinion (and consent) of Karen M. Muller as to the                  --
           validity of the shares of Common Stock to which this
           Registration Statement relates
 
  23.1     Consent of Karen M. Muller (included in Exhibit 5.1)                --
 
  23.2     Consent of Ernst & Young LLP, Independent Auditors                  --
 
  24.1     Power of Attorney                                                   --
E-1