When we travel, we take super shuttle or a cab. Often this is cheaper than driving and parking. It is alway more convenient and is safer, as a flat or car trouble is met with back up equipment. Could this be an alternative.

Also there is a FREE park and ride just off the Lakewood Blvd, near the 105 freeway. No real security, but they do have people there most of the time. The "train" in only $1.35? each way. Hard to beat. Also there are a few hotels that let you park for free if you spend the night before. I do this at Ontario, but also understand that LAX has some. Two months may be a problem.