I have left the airport during long layovers, both in LAX and other places. In fact, I am planning on doing it again on Saturday with a 6 hour layover.
I would have no problem doing it but would hesitate to tell any airline or airport employee about it. Once in Europe, the airline was hesitant to through-check my luggage when I mentioned I "might" leave the airport. They said something like "What if you don't make it back in time?" I don't think the US airlines are so paranoid though.
So just do it and keep it to yourself.