I can confirm that this was the case when I flew this exact routing with the same class mix (SYD-NAN in Y, NAN-LAX in J, holding Qantas Platinum status, FJ-coded tickets). We were not allowed lounge access in SYD as Oneworld Connect rules do not give lounge access for Qantas elite, unless flying on a QF flight number. Our tickets were revenue; when I booked I had QF-coded option but they were thousands more than FJ-coded, so we were happy to give up the lounge access and just buy something in the terminal.

We were allowed access to the FJ lounge in NAN ahead of the NAN-LAX flight as expected, based on class of service.