Does your child receive benefits from the education and participation package (http://www.bmas.de/DE/Themen/Arbeitsmarkt/Grundsicherung/Leistungen-zur-Sicherung-des-Lebensunterhalts/Bildungspaket/leistungen-bildungspaket.html) you get a subsidy for lunch at school. The remaining own contribution of the parents is one euro per day and meal.
Hamburg: For children, who are supported by the education and participation package, lunch is free of charge at all school types (http://www.hamburg.de/infos-fuer-eltern/4317736/mittagessen/).