It is the MSC that generates the Paging. In this Paging, the LAC of the MS is written.
The SGSN knows the LAC, it knows which MFS(s) is(are) in charge of this LAC. It just forwards.
The Gs interface means that there is a LA/RA combined update, so I’m quite sure that the SGSN won’t have a problem to correlate the LAC with the RAC. On top of that, I think that the SGSN *even without LA/RA update* knows about the Location Areas, since that is a part of the (global) RAI (RAI = LAC + RAC)