Ann: Litigation Update, page-94

if they deemed section 51 than that is legal
The Parliament shall, subject to this Constitution, have power to make laws for the peace, order, and good government of the Commonwealth.
but in doing so i believe this section will take effect
(xxxi) the acquisition of property on just terms from any State or person for any purpose in respect of which the Parliament has power to make laws;
under section 134 of the petroleum ACT
relevant part

or the holder of an authority may—

(a) apply to the Tribunal for the determination of a disputed claim for compensation in relation to private land or native title land (other than a claim for just terms compensation under section 53(1) of the Native Title Act); or

(b) refer a disputed claim referred to in paragraph (a) to the Supreme Court for determination—

in accordance with Part 10 of the Land Acquisition and Compensation Act 1986 as if it were a claim for compensation under that Act and as if the authority holder were the Authority referred to in that Part.

so I'm no judge or guru but i believe the above is the logical outcome
imo LKO will have to relinquish it's leases/permit what the compensation components are i have NFI