If you're worried about food, I'd recommend getting a proper (aka, non airline-lounge) meal before in LA, and then having perhaps some caviar, soup or maybe Chinese meal on board and conking out.

The Qantas F lounge is a great lounge at LAX, probably the best I've seen in the US. But I'd still take good restaurant in LA any day over eating there....it's still an airport lounge at the end of the day. I definitely wouldn't recommend a.) starving yourself in advance, b.) so you can eat at QF F LAX, and then c.) be full on the airplane. I'm presuming here you're looking for a "maximizing" effort.

Personally, I think the novelty of getting decent food (and a rather spectacular presentation, especially compared to economy or business class) in F at altitude is far more interesting and "WoW!" than having a free, fresh a la carte meal in an airport. Because that's really all the a la carte option is at a lounge....free, good food....but not "that's the best restaurant in LA" type of food.

On board, the absolute quality of the food is undoubtedly worse. It's food at 30k feet so on an absolute level, it really isn't going to compare with freshly grilled food or whatnot you can score at the QF F lounge. But really, I can get remarkably fancy dining anywhere and just pay a few hundred dollars for it. Literally anywhere in the world. Meanwhile, you most certainly cannot get a blinged out food presentation at 30k feet unless you're flying F or private, which is a far more rare occurrence for most folks. Just my 2 cents.