I'm assuming the OP will be inbound on AS, but that may be an unwarranted assumption.
As I posted before, there are only two ways to get to the LAX AC if you are not inbound on an AA flight (and I listed them).
The OP won't have access to any lounges in the international terminal (if only lounge membership is AC).
And zman is correct, of course.
The LAX Admirals Club is pretty close to the TBIT. No more than a 5 minute walk. But security lines at the TBIT can be hit or miss - I wouldn't wait until the last minute to walk over to the TBIT.