The LA class was never an official option. These subs are too old, too outdated and would have to be re-fueled.

There are now reports, that the RAN will get Virginia class submarines in the 2030s:
Australian Report on AUKUS Nuclear Powered Submarine Pathway
AUKUS Plan: Aussie Sailors to Serve on American Subs, RAN to Buy U.S. Virginia Attack Boats

There is also an article that Rolls-Royce will built the reactors for the RAN submarines:

Nuclear reactors from Rolls-Royce to power Australian submarines

This will be probably the SSN-AUKUS, the common future SSN for both RN and RAN - and these will arrive in the 2040s as to the original time schedule by the Australian government.