Yeah, that's called the Encounter but it's still undergoing renovations, and really isn't all that remarkable at the moment. Not the best place to stop. I hate to say it, but you are in for a pretty crummy layover at LAX
. I fly out of here almost weekly, and it's really a sub-par airport in today's modern commercial aviation--especially at redeye hour.
But since you don't have a choice and would like to make the best of it, perhaps you can dig on some plane spotting and use SkyMeals as a means to getting you a 4-star bite to eat (portable), and do a little plane spotting of the south complex via Imperial Hill.
SkyMeals can accommodate your arrival with a pretty nice menu, and they'll bring the food to you. Catch a cab to Imperial Hill and set a pickup time to get back. Shouldn't be too much trouble, especially with a 4 hour gap. SkyMeals website appears to be down at the moment for maintenance, but you can reach them at 1-866-759-6325 or visit the website via www.archive.org.
"The strength of the turbulence is directly proportional to the temperature of your coffee." -- Gunter's 2nd Law of Air