Do this a lot, generally 2 hours is plenty of time. If you are a US citizen, immigration is fast, if not it can be slow. I never check any bags so I don't wait for baggage, I just go to customs green line and leave.

US is in terminal 1, so you either need to take the shuttle bus (takes at most 10 minutes) or walk. If you walk go through the garage as it is much faster than walking all the way around. US shares terminal 1 with WN, so the security lines can be a little slow with families. So, don't hang around outside of security, clear through security and then relax.

US only has a couple of gates at LAX so it's a small operation. There is a club but it's very small.