In fact, I've read a thread where someone was asked to put his FF number in the reservation at checkin so that a lounge invitation can be issued. I think the same process would apply at the lounge where they might need to enter your FF info into the system to ensure that you hold the correct status before allowing you in.

I was able to change my FF info in the lounge at the service desk numerous times without problem. In fact, this is the standard practice that CX suggests people do. The only thing I would watch out for is at outports where the lounge is not operated by CX where they might not have the equipment to print out BPs.