So you're flying PDX-LAX-MEL-SYD-AKL? in F for LAX-MEL and J for MEL-SYD-AKL?

Do you have any oneworld status?

With a QF F boarding pass, you can use the AA lounge in T4 at LAX, but will need to take buses between T6, T4 and TBIT.

In MEL, you can use the QF J lounge. Entry is through the Qantas Club to the right after security.

Jetconnect is a 100% QF owned NZ based company. It is branded as QF and operates as/for QF. Jetconnect operates most of the QF trans Tasman flights. You can use the SYD QF J lounge for the flight to AKL. If it is the same day as the F flight or you have OW EMB, you can use the F lounge.