LAX is, by far, the fastest of all of the UA hubs to get through as an elite from start to finish. If there's ever a line at T6 security (which there usually isn't), the CO EliteAccess line is always empty, and they allow in UA elites. I've consistently breezed through front door to gate in 5 minutes - 10 max.
Once you know it, it's a breeze to get around.
- T