No, not all Lexus dealers give LOC discount, but the majority do.
Worth shopping around, you may find it's cheaper to drive to a more distant dealer, such as Hanley, and get it done there.
Alternatively why not get the timing belt & water pump done at an independent, then get the rest of the service (and the L stamp in the book) at Lexus?
Incidentally when the water pump failed on my Carina E, Toyota in Builth Wells asked me if they wanted the belt changed at the same time (as it had to come off to do the pump). The extra cost? About twelve quid, the cost of the new belt!