The Transport Statement in the planning application (PA/21/00678/NC) for change of use of the neighbouring building includes a map of these proposed cycle facilities as well as a map of local cycle routes under the Local Cycle Network heading.

Though that map doesn't show anything specific for the LCI estate (I assume the map pre-dates the development), it describes the connection to Leamouth Road and the C3 as: "the riverside walkway, off-road, to the west of the site joins with the CS3 at the Leamouth Road pedestrian/cycle crossing" (not explicitly calling it a cycle path, but suggesting it's a cycle connection).

On a related note, it also mentions the Goodluck Hope riverside paths as "walkways and pedestrian/cycle routes" ("This area is also being redeveloped at present for the Goodluck Hope scheme which includes additional riverside walkways and pedestrian/cycle routes")