My great aunt taught me the song in the 50's when I was very young. I remember the lyrics as follows:

Leprosy.
Good God, I've got leprosy!
There goes my eye ball
Into my high ball.

My upper lip
Just fell in the onion dip.
(I forget the rest).

(I would give anything to know the rest of the lyric if there are any. However, I notice that most people's recollection ends at about this point as well.)