Flying in the morning I try to take flights that are no later than 9 am, because if it's later than 9 am the traffic to the airport will have increased enough that you need to leave at the same time as if you had a 9 am flight. But I have to to through downtown LA, so that's a lot of what causes the big increase.

It can be quite crowded at 10-11 pm - according the the LAX facebook page and various articles, peak traffic is 5 pm to 11pm, with Sunday particularly bad (people arriving home from weekend trips). Around the holidays it can be a nightmare til midnight or later- I've been stuck in traffic on the 105 with it taking an hour to get from the 105 to T1 at ~9pm a week before christmas.

And as Colin says, the LA part is at least as important as the LAX part - once you're in the horseshoe you can either walk (it's a short walk from T1 to T6/7/8 across the top of the U) or you can hop on a LAWA terminal connections bus that now cruises in a dedicated bus lane.

But LA traffic is far from non-existent after 10 pm, depending on where you are and where you're going. Around the holidays the traffic into LAX will be bad after 10pm, and various parts of LA can be congested at nearly any time of night (3 to 5 am is probably the best bet for low traffic)