Um, wow. Ok, twenty minutes limits you geographically, and vegetarian also is a limitation of sorts. But price is not a consideration…
It does sound like a great get-together though! Assuming your vegetarian friend is okay with eating chicken/fish, here’s what I suggest, off the top of my head:
The Chart House on Panay Way in Marina Del Rey. It’s a chain, and quite upscale, but the food is decent and it’s by the water, which is a lovely place to be this time of year. If you’re all okay with a chain that’s a bit cheaper, Cheesecake Factory and El Torito are in the vicinity as well. Marina Del Rey is as far north as you want to go, because after that getting to Venice/Santa Monica either means going round on the 405 or heading north on PCH/Lincoln, neither of which is under twenty minutes (especially Lincoln!).
A lot of the restaurants on/around the beach/beach cities are overpriced and overrated, but there’s several restaurants on Washington Boulevard in Marina Del Rey, the last ten blocks to the ocean; you could just drive there, park, and walk around and pick one. My favorite restaurant in Marina Del Rey is Tamara’s Tamales, but it is a hole-in-the-wall, and not a good place to linger over your meal. Good tamales, though!
Petros Greek on Manhattan Beach Boulevard in Manhattan Beach is decent, and not too far from the airport. Manhattan Beach is about as far south as you want to go on PCH, otherwise, it’s over twenty minutes sometimes. Greek is always a good choice with a vegetarian in the party, because there’s a mix of meat and veggie choices on the menu.
If you’re there in the morning, again, you can go to Coffee Company as I mentioned earlier. It’s on La Tijera, a hop, skip, and jump from the airport.
It’s a bit too expensive for my taste, but @YARNLADY‘s suggestion of The Proud Bird works too, since they have seafood and pasta along with the beef.
Finally, @jaytkay‘s suggestion of staying at LAX and going to The Encounter saves time for whoever’s flying in/out.
That’s probably the best I can do. The better quality restaurants (in terms of food!) in L.A. are not in the LAX vicinity. I’m surprised @Brian1946 hasn’t offered a suggestion; he’s been in L.A. longer than me and may have better suggestions.
Good luck picking a place, have fun!