What happens if something goes down like a lead balloon?
Well, it falls very quickly.
It's a phrase to describe something that is badly received. For example, a play or a film. In work or social environments it could be a presentation that goes badly or a joke that doesn't work - so be careful what you say.
Of course, lead is a heavy metal so a balloon made of it would fall from the sky. It was probably the inspiration for another kind of heavy metal too.