Think OP wanted to have the BP and lounge invitation from OLCI to access the oneworld/QF lounge before CX counter opens?

If OP is arriving LAX via AA or AS and has sapphire, emerald or is holding F or J ticket, I would say maybe use the AA FL first before CX check-in counter opens. You may also want to try your luck at the oneworld/QF lounge to see if they can process your entry (or even check-in, though I doubt) for you.

Last year, I arrived ORD on an AC flight, connecting to JL. I didn't have boarding pass as AC couldn't print it, but AC checked my bags through. I presented my ticket at the Admirals Club, who had a JL agent stationed there, and she completed the check-in for me at the Admirals Club.