I made a bit of progress here (even so nobody from SAP has even looked at my ticket yet).
Whenever trying to start LCA, it throws an exception of "CX_SY_NATIVE_SQL_ERROR":
Procedure LCA_LCK_LIST_OWNERS -> Synchronization of the Lock Owner of the liveCache Lock Server
I had restored the entire LC DB from source from scratch again (just in case something went wrong last time), (re)set the CONTROL, SUPERDBA and <SID>ADM passwords manually, did a systab load (Source: MaxDB v7.7; Target MaxDB v7.9) and brought the whole thing db_online w/o errors.
I double checked that I could logon with all the relevant MaxDB users with the specified password(s) on CmdLine, and sync'ed the integration data for all connections correspondingly in LC10.
Still, its all to no avail, so I start to question if LC is compatible with MaxDB 7.9???
PS: Thetests in DB59 work just fine for all connections - honestly I'd be happier if they wouldn't, cause it would help me narrow down the root cause of this mess.