I ate lunch here twice and found it to be pretty good. They have some appetizers and sides that can be made vegan, plus about 4 of their pasta sauces are meat-free and dairy-free (there is a tomato and olive oil sauce, an arrabiata sauce, an aglio e olio sauce, and a lemon sauce).
Some of the pasta is homemade and may contain eggs (my German is VERY limited and the waiter seemed to have a difficult time understanding my questions about the contents of the food, so you may want to check this for yourself) but the spaghetti does not.
The service is relatively quick. The indoor section is non-smoking but the outdoor section allow smoking, so you should ask to sit away from the window if you don't wish to be close to the smoking section. Santa Lucia is by no means a vegetarian restaurant, but it is a nice place to go with non-vegetarians friends who don't want to be dragged to Hiltl and Tibits for every meal.