Neustadt is the most often used name of cities in all over Germany. The following cities are somehow larger than others:
Neustadt in Holstein
Neustadt an der Weinstraße
Neustadt am Rübenberge
Moreover some city districts are also named "Neustadt", meaning the relatively younger part of a large city, such as Hamburg.
So be clear about which Neustadt you mean. Otherwise you end up researching in some 30 cities all over Germany.
Correct spelling might be: "Lünzmann"