AM14 is a practically located vegetarian restaurant in Luxembourg City. It is in the same building as Luxembourg City Museum in the Old Town. It is more like a cafe than a restaurant, dishes are mostly behind a glass and cold. About half of the dishes were vegan: wraps (named kebab), noodle dish, cous cous salad and gazpacho soup. The only vegan desert was also raw and not very appealing, but the self made looking vegan ice creams might have been good. I had a wrap and soy cappucino.
Luxembourg City has amazing views because of the canyon that surrounds the Old City. Also AM14 had great views.
There would have been a few more vegetarian restaurants in Luxembourg and one of them, Anabanana is located close to the Old Town too.