http://www.lawa.org/lax/laxvaletparking4.cfm
Wasn't aware of this perk until I saw the sign last time at the airport. Here's the information:
Valet parking is available in the Central Terminal Area on the lower/arrival level across from Terminals 4 and 6. The Terminal 4 lot is convenient to American Airlines in Terminal 4, Delta Airlines in Terminal 5 and 30 airlines in the Tom Bradley International Terminal. The Terminal 6 lot is convenient to United Airlines in Terminals 6, 7 and 8. The cost is $38 per day or $10 per hour up to the daily rate.
Alternative fuel vehicles with a state-issued sticker allowing the use of the freeway carpool lanes pay $30 day, the daily rate for all Central Terminal Area parking.