According to my waiter, the following menu items are/can be made vegetarian:
-Some of the ensaladas (salads)
-Roasted poblano relleno de queso (contains cheese)
-Spinach enchiladas (contains cheese)
-Beans and rice (but not the Mexican rice, which is made with chicken broth)
-appetizer (I can't remember what it was called!) that consisted of potatoes which are smashed into round cakes (about the size/shape of standard falafel), coated in cornmeal and fried (in vegetable oil), served with guacamole.
The beans and rice and the potato appetizer that I mentioned above are both vegan (although you need to specify "no cheese" on the appetizer). The potato appetizer was a wonderful treat. The beans and rice were pretty decent (though admittedly not very exciting).
Also worth noting: The outdoor seating area is beautiful. The restaurant was consistently crowded and the waiters were very friendly (and enthusiastic about naming off the vegetarian items). There is an extensive frozen drink list. Overall, I had a very pleasant experience at La Fonda on Main.