With a Luxury (LCAR) selected, you should be assigned a vehicle with the option to pick from the PC area. If the location is not assigning you a luxury car in a specific space, they are not following the guidelines for the Ultimate Choice program. The reason is that while Ultimate Choice can often have a great selection, there is nothing that guarantees there will be a Premium or Luxury car there when you arrive. If you book an ICAR-FCAR you should be sent to Ultimate Choice (and Presidents Circle section if you have status) to choose.
If you book anything other than that (or an ECAR/CCAR which has their own sections) then you should be assigned a vehicle in a specific space. If this is not happening you should:
a. Complain to the location
and/or
b. Stop booking LCARs and just book ICARs since you can choose from UC anyway (although not from the PC section unless you have PC status)