Vegan and Vegetarian are on the menu, but the same kitchen also prepares what you avoid, so cross-contamination is possible. Tell staff what you react to, and ask how your dish is prepared before you order.
The Neubau counter of Karma Food, a Vienna lunch kitchen that calls itself Indian, vegan and authentic: curries, dal, bowls and a weekly menu, with catering it describes as vegan and veggie. The site makes no organic claim we could find, so ask about ingredients, the kitchen has the final word.