Do you want anything in particular?
My go-to place for this area is Luna Park, just north of Wilshire/La Brea. Great food and not too pricey. Cool atmosphere. And it is much less insane and more relaxed during lunch than at dinnertime.
Just west of the Pico/La Brea intersection is a Roscoe's chicken & waffles which I love. Inexpensive and very casual. It's one of the larger locations too, so the wait for a table isn't very long.
la maison du pain for baked goods and sandwiches. i believe they have quiches as well. mmm quiche!
Chulada Grill at San Vicente and Hauser has good tacos, some Oaxacan specialties, and kick-ass pico de gallo in the salsa bar. They also deliver.
I posted on Rubio's Bakery (Guatemalan) right across Pico from Lucy's:
It's got a food counter w/ hot items, but generally very fresh. Unusual stuff if you're used to run-of-the-mill Mexican food. I agree - it's not a particularly chow-ish zone.
Isn't there a Oaxacan place right in the same strip mall? (maybe confusing it w/ another loc.).
I live around that area so I have been looking for good lunch spots as well.
You could also try Pasquale's Cafe: 5616 San Vicente Blvd. 323-933-0755. It's a cute cafe with a nice little courtyard patio. Otherwise I second the recommendation for Bloom Cafe. If you go a little further north to Wilshire and La Brea there is a nice sandwich place called Panini Grill, 5354 Wilshire Blvd. 323-935-0237. Or also right off of Wilshire you could try Back Door Boba Cafe, 5484 Wilshire Blvd. (rear) 323-933-4020.
I'd be interested to know of any other great spots around the area as well.