I hope you will have carry on only or a single ticket for the connection.

Rechecking bags from BA>AS at LAX without having a single ticket and BA tagging the bag all the way through could result in having to walk from TBIT to T6 and check them in with AS. This happened to me a couple of years ago as AS did not have agents at TBIT for bag tagging and check. The walk was not something I enjoyed using a cart with narrow walkways, construction, and a number of cell phone zombies blocking the access way; also as bad luck would have it the first set of elevators from arrival to deprture in T6 were under repair. In this case you would be going for the long walk 3 times to access QF lounge in TBIT

I never tried this with BA, but remembered they how they refused to check through on separate tickets.

Cheers,

-Cyborg