The only published caveats in relation to Qantas lounge access being dependent on having the frequent flyer program providing status based lounge access entered into the booking relates to EK elites .
e.g.
Qantas First lounge - Melbourne
Emirates Platinum Skyward Members
Next onward flight must be operated by Qantas^ or Emirates^ with a QF or EK flight number.++ ...
^ Lounge access eligibility is based on ... the Frequent Flyer Membership tier for your next onward flight.
...
++ Flights to Americas and South Africa are not included.