Ralph later did his homework and then told me I might find this number enjoyable if I looked for it on You Tube.
It turned out that Meet Me by the Ice House, Lizzie was made famous in the 1930s by the Hoosier Hotshots. The Hoosier Hotshots (based in America) seem to have combined vaudeville with very good musicianship (including some unusual home-made musical instruments) to produce comic song recordings that were popular through the middle of the Twentieth Century.
According to one source, Meet Me By the Ice House, Lizzie was composed in 1935 by someone called Cletus M. Wickens.
So I listened to the song performed on YouTube by the Hoosier Hotshots and I had to agree it was a very attractive, amusing number, and well suited to traditional jazz. This is mainly because it has a simple 32-bar structure (16 + 16 [no Middle Eight]), with an elementary chord sequence. Its words are of course comical, so adding a vocal - if your band has a willing singer - would be fun too.
I tried to work it out by ear and came up with the following lead sheet for Meet Me by the Ice House, Lizzie. On the recording, The Hoosiers perform it in the unusual Key of D; but I have put it into F, as this is more comfortable for me on the cornet.