Originally Posted by
serfty
As already indicated, there is an airside connector between T4 and TBIT that opened recently.
Before that, since May 1st, 2014 airside access at LAX for any terminal has simply required your boarding pass and ID for a flight departing that day from any LAX terminal.
So, even if departing from T2 (for example) you can still get airside at TBIT your T2 BP. Or, say if an A/C member, that T2 BP will get you access to the T4 A/C.
The question was about lounge access after an arriving flight, so the passenger would not have any boarding pass departing LAX. As you say, moot point because of the connector anyway.