Not 100% sure, but I believe it is only Galleries First and Galleries Club, so somewhat like the old T1/T4 set up. This might be largely down to the fact that there will be relatively few First passengers on a daily basis. These lounges will be BA/QF branded and be in addition to the existing OW lounges.....at this time.

Given the current financial situation all airlines face, I wouldn't be surprised if at some point in the future there is a larger OW lounge, it would make sense to some degree. Would seem to make sense given the existing facilities at LAX.