What Is The Joke About The Dog Who Stands Up At The Piano And Plays "Melancholy Baby"? [possibly NSFW]

Source of my curiosity:NPR

Google fu has revealed drunks shouting play "Melancholy Baby" at concerts preceded shouting play Freebird. There is a joke where a drunk shouts "Play Melancholy Baby", and the singer says "I don't know that one, any other requests?" and the drunk replies "show us your tits" (Or junk if the performer is a man).

There is also a Calvin and Hobbes joke about mixing a cantaloupe and Lassie to get a "Melancholy Baby"

But either of these jokes are missing both the piano and dog playing Melancholy Baby.