score:4
I have arrived in LAX with an E3 visa, a wife and two children (who all had E3-D visas) before. And it all depends!
If you are lucky, and you get to immigration and there is no queue, then you will need 5-7 minutes to get through your immigration officer.
The thing is, if you're flying Qantas, then they fly A380's into LAX, often early in the morning. Which means there are a lot of people to get through immigration. And if you're unlucky enough to land at the same time as another A380? Well.
For what it's worth, the average time for me to:
With an E3 visa and dependents is around 2 hours. The worst I had is 3.5 hours, but that was with a long immigration queue and a mixup with the boarding passes for my next leg.
I would say that 2 hours is pushing your luck. I once took QF12, which is SYD > NYC with immigration through LAX and I heard my name being called as I ran down the terminal to get to the second leg of the flight (sorry, I was that guy. But it was't my fault, I got "randomly selected" for having all my shit inspected at TSA).
However, the best transit time I've ever had was 30 minutes. It was almost too good to be true. First off the plane, first through immigration, first through customs, empty TSA queue. I spent more time walking between things at LAX than I spent in queues. However this is exceptionally rare.