There are 4 or 5 different BA/QF joint lounges in LAX. It depends on the class of travel and which flight you are on.

They are all pretty much the same. FC has a little better food but not by much. Overall, the lounges are nice when compared to other international lounges. Very nice when compared to the regular red carpet club or admirals club.

I don't think you will be able to bring your parents in. You need to pass security and they normally check your boarding pass before security. If they are not flying, then they probably cannot make it to the air-side of the terminal.