Gluten-Free, Lactose-Free, and Vegan 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.
Pia's Wohlleben in Vienna's fourth district serves over 30 homemade organic Spätzle dishes, which the site says can all be ordered gluten free, lactose free or vegan. The menu notes that traces of gluten are possible in the gluten free Spätzle, and staff give information on allergens. Tell the staff about your allergies, the kitchen has the final word.