You'll want to allow a good chunk of time for TSA. I've been through it quickly (less than 15 minutes), and not so quickly (an hour on a Sunday afternoon). Two years ago, I flew out of a different airport (PDX) on a 7am flight on a Wednesday, and, holy cow, I was shocked at the TSA lines at that time. 4:45am and there were LOTS of people on there. Point being, it's kind of shocking how many people are flying out at 6-7-8am on random weekday mornings, and LAX is a busy busy place, so I'd plan on an hour at TSA. If it's less, then yay! If it's more, then you have built that time in and aren't going to fret about missing your flight. Or maybe it's just me--I had to run for a flight once, totally thought I was running on time when they did the final boarding call--so, I really plan that everything is going to take longer than it should!