Yes you can stay airside.
Even if you can't check in for your OZ flight online, if you bring a printed confirm, that should get you into the *A TBIT lounge. Then you can go to the gate to get your boarding pass somewhere inside of T-2.
Though with 8 hours, I would leave the airport and go to Manhattan Beach, Venice, or Santa Monica. That's WAY too long to spend airside at LAX.