They seem to be working out the kinks of no invite cards. The evening I was there (October 15), there were several passengers who had connected and already had their boarding passes so had no need to check in at LAX. The bus agent was figuring out a procedure to log their lounge visit to the proper airline so they could go out without a card. I suspect they will have a system to handle this soon. They seemed surprised at first that someone could have checked in somewhere besides LAX.
I think the airlines at TBIT are well aware of the need to issue lounge cards and SQ at least had a detailed sign explaining who got access where and that cards were required.
Charles