A joke from the original! Which is why it’s a direct takeoff on a line in Greatest Show on Earth instead of, you know, some stuff I made up.
It is not clear to me whether Lance hurt his arm in some non-cutting way–e.g. dislocated–and got it covered in greasepaint as well, or whether he is actually bleeding greasepaint. The intention in the original was definitely the latter, I think. You may choose to believe what you wish. I think both are equally viable in this plane of reality.