We were flying LAX -LIB a little over a week ago when we were denied immediate access to the Lounge and placed on a waitlist because the desk agent said the lounge was nearing capacity. I can't find anything in the published rules regarding how access priority, if it exists at all, actually works and am wondering if the agent might have just gotten their knickers in a twist.

I'd forgotten we were flying paid long haul first when I presented our boarding passes so I also gave her our Admirals Club card. That's when she said the club was nearing full and they had to hold space for AS club members. It was only then that I remembered we were on paid F and told her this but she said that made no difference and that our only options were to either go to the AA club in the next terminal or be placed on the WL. We opted for the latter and were cleared about half an hour later.

My question is where anyone knows if the agent was correct that the rules require or permit them to hold space for subsequent AS club members who might show up after a passenger presenting either an Admirals Club membership or a paid first class ticket.

To be clear the agent explicitly stated they were holding space and not that the club was actually full.