This is a clip from the Colgate Comedy Hour that aired live on November 13, 1955. It was one of the last times Dean Martin and Jerry Lewis hosted that show and it was a little over seven months before they made their last appearance as a team. So despite all the on-air buddy-buddy rhetoric, they were probably already close to splitting and weren't palling around a lot off-stage.
The song is "Two Lost Souls" and I'm not sure whether it's ironic or appropriate…or maybe both. But it was from the play Damn Yankees, which had debuted on Broadway six months earlier. Some lyrics, obviously, were changed for Dean and Jerry. A little less than forty years after this telecast, Jerry would make his Broadway debut in a revival of Damn Yankees…and he would sing "Two Lost Souls." Interesting? Kind of.