I adjusted the street names and layout a bit from VZD cadaster data. A couple segments that have street names do indeed enter private/closed industrial area. This is not unusual. The actual way in OSM would get classified according to use - for example, service + private, and we can still add the name. There is a Sprīdīša iela section in industrial area, although not where the note point is located. There are no streets or street borders in the cadaster data there. We can draw some service roads from aerial here, but they wouldn't get a name. Your original map is most likely either out of date (there may have been a street here long ago) or was incorrect to begin with (not unusual for random side streets to get wrong names in various maps).

P.S. You can use https://lvmgeoserver.lvm.lv/geoserver/ows?FORMAT=image/jpeg&VERSION=1.3.0&SERVICE=WMS&REQUEST=GetMap&LAYERS=public:Orto_LKS,publicwfs:Kadastra_karte,publicwfs:arisstreet,publicwfs:arisroad,publicwfs:arisbuilding&STYLES=&CRS={proj}&WIDTH={width}&HEIGHT={height}&BBOX={bbox} as map background to see cadaster data on top of LVM aerial.