According to Index Fungorum L. naucinus has not been deprecated in favor of L. leucothites. Only Lepiota naucina var. leucothites has been so synonymized. I don’t know the technical details of what the differences are supposed to be between these two species. These species are synonymized in Swiss 4 with L. leucothites taking precedence. For now I am leaving them synonymized, but with both names considered valid.