After much research of finding the cheapest LAX Parking, I think I've finally found it. Longer stays at certain parking lots are discounted.
Sample parking fares not including 10% tax (all have free shuttle to/from LAX):
Lax Parking Lot B is $8.00 per 24 hour period
Lax Parking Lot C is $10.00 per 24 hour period
Johnny Park (Next to Lax Parking Lot B) is about $8.00 per 24 hour period.
LAX Self Parking is $4.50-$5.50 per 24 hour period for rooftop parking (7th Level). It's a hassle to drive all the way up to the rooftop with a limited number of spaces and sometimes all the spaces are taken. To park indoors, it is $6.50 per 24 hour period. You can see the current rates on their coupon section of their website. You have to print the coupon to get the rate www.laxselfparking.com/coupons.html and show them the coupon before you park. Also, the rates changes every so often whenever you go on the website (you can see the dates the coupon is valid for) , but are still cheaper than other lots.
Easy to find on LaCienaga / 99th street (north of Century Blvd). Shuttle service is sometimes terrible (varies) and it may take up to a half-hour waiting at lax (going to lax is not as bad at approximately 10 to 15 minutes wait; similar to other lax parking lot shuttle services. Close to LAX.
update as of 4/9/08 - $5.95 is cheapest for rooftop parking on coupon, so not as cheap as before but still reasonable.