Depends on the departure time. The LAX Polaris lounge was absolutely bursting at the seams when I was in the late night departure bank (for Australia).

Regarding the latest questions: yes, you do have Star Alliance lounge in TBIT, but I am pretty sure you can only access it once you clear immigration and check back in at TBIT. There is no such thing as sterile connection from international to domestic in the US - you always have to clear immigration/customs, then re-clear security. You can walk to TBIT to T7 airside (maybe landside indoors too?), although it’s somewhat of an unwieldy haul. If it’s nice weather out, I would rather do the walk outside, which is what I did on SYD-LAX-EWR many years ago.