At one time (2 years ago, and this may still be the case) the LAX Parking Authority, Located under the Parking structure across from Terminal 1 or 2. (it used to be called 5 Star Parking), would sell yearly passes for the Employee "B" Lot (111th and Aviation) for about $130/yr (Cheap!).
Be nice and explain that you FLY (not commute) out of LAX and would like to get an Annual Employee "B" Lot Pass.
Give it a shot It may still work. The "B" lot has buses that run every 10 minutes 24 hours a day and the "B" Employee Lot is located just behind the regular "B" Lot parking, an easy walk to the buses. Plenty of Security, I parked there on and off for 15 years and never had a problem.