I don't understand how acquiring small numbers B777-200LR specially for the ULH routes make sense.
Sure the purchasing price might be extremely good. But in order to make sure these project became successful, they have to use the most efficient aircraft they could find.
Cheap aircraft only works for short flights with high cycle. Or when the plane have decent fuel burn (not the most efficient but efficient enough to operate).
And B777-200LR isn't in that category.
You measure performance two ways.
1) Fuel burn per passenger using the same seating density across all aircraft.
2) Fuel burn per kg of payload weight that can be carried on the route.
The 777LR is actually very competitive on number 2 and it can easily do the project sunrise route. Fuel burn per kg is probably the more important measurement of the two.
The 777LR can carry more payload weight on that route than both the 777-8 and A350-1000. If you simply fit all three aircraft with similar density cabins then the 777LR will look bad and burn 15-20% more fuel per passenger as it has the smallest cabin. However if you look at fuel burn per kg of payload the 777LR would be very close to the newer aircraft and may even match the A350.
I estimate the following max payloads on the LHR-SYD route:
777LR 35t payload
777-8 30t payload
A350-1000 25t payload
Now the A350-1000 will have the lowest trip fuel burn, but the 777-8 carries 20% more payload. As the 777-8 will not burn 20% more fuel it has the lowest fuel burn per kg of payload. Same deal with the 777LR it will have the highest fuel burn but carries the most payload.
The economics of the 777LR look amazing when fuel prices are low. I'm surprised Qantas didn't purchase it a decade ago. I'm fairly certain the GE90 has had a PIP since Qantas last looked at the 777LR.
This is why an aircraft like the 787-8ER looks so attractive on paper. It might carry three quarters of the passengers while burning three quarters of the fuel but the big advantage is it could carry the same payload weight of the bigger aircraft while burning three quarters of the fuel. That adds flexibility for a denser cabin, put toilets below deck, more headroom for bad weather or extra express cargo.