I stayed at the Westin LAX over the Christmas break. The lounge was closed for some reason (renovations?), but the Westin had a small room set up for their Plat's offering a hot breakfast. It wasn't elaborate, but had 2-3 hot entrees and a 2-3 cold offerings.
There is a Denny's about 5 mins walk from the Westin LAX towards the airport if that helps.