I had read about this place on happycow, and here's my Figtree's Cafe review. This beach front restaurant has been operating in Venice Beach, on the boardwalk, for many many years now... I've eaten here a couple times in the past and was just here again in January 2012.
Figtree Cafe offers a 50% off discount deal on your breakfast bill between 8-9am everyday. The breakfast menu is ovo-lacto vegetarian friendly, but for vegans the choices are limited. You can ask to substitute soy cheese (not sure if contains casein or not), and there is a tofu scramble main dish. You could also get a fresh fruit plate, and a bowl of steel cut oats with fresh fruit.
For lunch and dinner, there are several ovo-lacto vegetarian choices plus a couple vegan ones.
While Figtree is not pure vegetarian, it is an option for sitting down to enjoy the ocean view and watch people walk by. The food taste is all right.