Having just arrived at LAX this morning from QF11 there is now a new line for express clearance.
This only applies to people with ticketed connections, and I think I heard the airport staff saying 90-120 minutes or less.
After you leave the aircraft, if you see a ground agent they will give you an Orange/Yellow card to use the express immigration lines.
(obviously you need a boarding pass for the connecting flight)
I was sitting in 13A on the 388 and was the 3rd or 4th off the aircraft, there was another passenger in the front J section who got one of these express cards after deplaning, and they were through both Immigration, with priority bag collection and then through the express customs line in less than 10 minutes.
Mind you, I think it only took me 25-30 minutes for me to be landside waiting for the hotel shuttle bus.
This is a very positive move in what is one of the worst US airports to clear immigration and customs, especially during the peak arrivals times (personally have waited 2 hours in the past to be landside after arrival at the terminal... that sucked)
HTH