I'm not sure about LAX's restaurants, but I usually find that Au Bon Pain has the best airport food. I think it's because it's coldcuts and their staff assembles the sandwiches at the airport.

If LAX has one, I'd totally recommend it for airport food. Au Bon Pain's stuff is pretty much guaranteed to be actual food, as opposed to most of what one can find (after it's defrosted and microwaved) at airports. Au Bon Pain's orange juice is also extremely delicious.

Au Bon Pain is also pretty reasonably priced for airport food, in my recollection.