Actually now that I think of it I'm going to be in LA next Saturday as well. AA has IAD-LAX r/t's at $218.70 so I booked a bunch of them several weeks ago.
I'll be arriving at 11 a.m. or so on Saturday the 25th and returning on the redeye Sunday, and would be happy to do a late lunch, preferably somewhere on the Westside or Manhattan Beach area (not sure where i'll be staying yet).