Pretty much at every Indian restaurant you can eat vegan food. LA doesn't have a 100% vegan Indian restaurant, but we do have 100% Vegetarian. The main hang up is that its hard to avoid the butter... The cooks will put it on the bread and in the rice. It helps to have a server who is hip to veganism. We have the best time at Chandi in Santa Monica. You can even order your food Oil Free! That way you don't wake up with zits the next morning and a spicy oily slime over your body as it tries to exit all the fat from the Indian oil slick you consumed.
I've heard Paru is a good place, but the menu doesn't look too vegan friendly to me. Please offer up some suggestions and pictures rock!