There isn't a BA lounge in LAX, and there hasn't been one there in recent years either, just the Qantas one in TBIT. But yes you can use it, even if your flight is in T4 or T6 (bit of a hike to the last one though) and certainly for TBIT services. The LAX T4 Flagship is in reduced standing at the moment while it gets rebuilt. I was surprised to see AA1058 going from TBIT, it may change to T4 tomorrow.