You have some decent suggestions on how close you can cut things, but we don't know if there are reasons you would want to.

Yes, you could probably make your flight arriving at your terminal 1 hour before your flight, but why risk it, especially with the vagueries of L.A. traffic? You can run into unexpected delays at any hour. Plus, as you are driving you need to add the time either to return your rental car or find a parking lot for your own car. You do not state if there is a time before which you cannot leave (e.g., a meeting). Why not leave at 1 or 1:30, or even earlier, and have a relaxing lunch at LAX (e.g., at the Encounter restaurant in the middle of the airport)?