Originally Posted by dhuey
For around $50, you could probably get a *** star LAX hotel on Priceline (w/ shuttle).
Note: this would be for the "night" before your arrival, and you would definitely want to call the front desk to inform them that you'll be checking in really late.
This is a MUCH better idea than my previous suggestion of buying a refundable AA ticket and using it, plus $50, to access the Terminal 4 Admirals Club.
Bid $40 for a 3-star hotel near LAX (around $50 with tax) and you'll probably get the Sheraton or the Marriott. As dhuey said, be sure to call the night before so they won't cancel you as a "no-show" and once you arrive at LAX, hop on the shuttle and head to your room for a shower, nap, or TV.