I don't think that it is from "American" at all. This name is from the word "moon". I don't see any resemblance to Lucine and moon. It's most likely from Latin (Luna) or at least French (Lune).
Um, well, I'm 1/2 Armenian and I can tell you for a fact that Lucine IS the Armenian word for "moon" or "moonlight". I believe the two are very similar sounding.