Leip's little book, "Die Laterne,Lieder und Gedichte" has five verses to Lili. Mine is dated 1942 (20th thousand) but the first edition was about 1937-1938 probably the first printing of this verse, as Wolggang says. I have found offers of one or two of his pre-war volumes of poetry, but they are expensive.
Is he the same Hans Leip who, after the War, wrote (about 1957 for English editions), "The Story of the Gulf Stream"? It, and other books by this author, sold very well in translation.