Sheraton Delfina in Santa Monica
there is a oaxacan place on pico near 4th (I think it's called El Tejate). It's pretty good, but not great. i've eaten there a couple of times and not been wowed, but not disappointed.
Also, I've never been there, but I hear that the bowling alley just west of El Tejate actually has a decent diner in it.
Walking distance (5 minutes walk)
Catch at Casa del Mar
Chinois on Main
Whist at Viceroy
And there are two new wine bars with very good food in that new complex at Main and Pico(ish) - one's got two names, one has the word L'Orangerie in it, and is painted orange. Anyone?
And -- I like The Galley. Maybe only me, but I like it there.
OP - Delfina is actually at 4th, not Lincoln, and you have many choices.
You are probably thinking of Gouda & Vines (my impression was more sandwiches to go rather than dine in) and La Grande Orange--odd menu in some ways (sushi rolls, a burger, tacos, "six essential salads," "Dixie pan-fried chicken" and scattered other entrees). I tried the chicken ($17) and it reminded me more of "Winn Dixie" than Dixie. Going in another direction, literally and figuratively, Tommy's at Lincoln and Pico is a branch of a well-known local fast-food place noted for their chili burgers and dogs...albeit often more with nostalgia in mind. Moving back to the West, The Lobster (just South of the Pier), Ivy at the Shore (I'm not a fan but some seem to like it) and Il Fornaio (decent chain Italian) are all an easy walk down Pico with a short jog up Ocean to Colorado.