I don't know much about LAX, but I thought that all International Arrivals came into the Int'l terminal... I guss there are exceptions.
If I recall correctly NW and KL operate from T2 and T1 is HP, WN and US.
I just flew into LAX on HP a few days ago. For your benefit, the gate area is pretty spartan with a McDonalds and some sort of "aiport sports bar." So, if you're looking for a bite to eat and you see something to eat in T2 (or Int'l) then I'd suggest grabbing it when you see it.
Also, there's a US Air Club before security in T1. I've seen a few US Air Club passes on the CC w/ expiration dates of 6/30. The closer that date comes, usually more of them find their way onto the CC... just a thought in case you're delayed, etc.