PS (to my previous post):

TJ in San Diego - it definitely pre-dates Tom Lehrer, who never recorded it in any case.

Jon Stone - the tune goes back to the 18th century, apparently.

Lighter - interesting about Oscar Brand. If you can find a source to back up what you say, you should update the Wikipedia article. Funnily enough, Brand is also credited as the author of "Three Ladies" at All The Lyrics.com. But I believe it goes back to the 1930s at least because my mum says she sang it as a girl back then (unless she's misremembering). And I'm sure it must have started life in England and that Brand is unlikely to have written the first three verses.