Getting ahold of someone for info is a joke. It's pretty strait forward once you do it so hopefully this will help. I just went through the process last month.
http://www.lawa.org/Uploadedfiles/LAX/Parking/LAX_Employee_Park_Permit.pdf
(The only thing that is really good for is the little map)
Go to the east lot, tell the guy/gal that works the gate you want to buy a permit for the month and he'll let you through. Pull up to the trailer that's parked in the south west corner of the lot and tell the person working you want a pass for XXX month. All you'll need when you get there is your airline employee crew badge and $55. From my understanding there are 3 lots. West, East, and South. I went with the South lot because she said that all the busses stop out front for pick up and drop off, so you can get to any terminal from the south lot.
A few helpful tips-
There are multiple busses that pull up to the stop that only go to a range of terminals (ex. Terminal 1-5 bus and a 6-8 bus) so pay attention to the electronic sign as the bus is pulling up to make sure it will go to the terminal you need.
They will only drop off and pick up from the upper level. So when you get home from your commute, take the escalator up to the departures and wait by one of the 'employe bus pickup' post on the side walk. Feel free to message me with any other questions. I was pretty lost the first couple times I tried it.