Mondays are usually tough at the airport for security. I would not arrive any less than 90 min. That means 90 mins from the point in which you step into the TSA line. Not 90 min from the time you arrive in the greater LAX vicinity with rental car, shuttle, etc to still deal with.

With respect to the drive, that's a tough slog as you'll be in traffic most of the way. There are certainly a few route options and carpool lanes but you can still expect quite a bit of traffic.

Traffic starts pretty early around here. When I've been on the road at 530am to catch early flights, I was astounded at the number of people on the road at that time of day.

If it doesn't create hardship on your trip, staying near LAX the night before is a great idea.