geo1004 - I saw a dedicated BA lounge at LAX, which I believe is for Business Class or elite Executive Club members. Then there is this shared BA/QF lounge I was in. This may have been the first class lounge for BA and QF, but like I said, I was directed to this lounge when flying BA Business Class earlier in the year (maybe the J class lounge was getting full, so they sent me to first. I don't know).

I did not see an actual Qantas Club on the lounge listing in the elevator. The only thing listed for QF was the joint BA/QF lounge - which may just be the 1st Class lounge.