I am assuming that the correct spelling would be "Lünzmann", there is a small likelihood, that their original spelling was not altered.
I looked up the German phone book, and found 118 Lünzmann entries. 18 of those are and the ZIP code area "2" (= North Germany), however none of those is in the Neustadt/Holstein area today. I have not found any with the spelling "Luenzmann".
By the way my former boss was also a Lünzmann, her name is Monika, she is from Hamburg, but works and lives now in Hamburg.