Here's my transcription from the recording at Honking Duck:

DO ROUND MY LINDY
(As recorded by Fiddlin' John Carson, 1926)

CHORUS: Do round, my Lindy. Do round, my Jane,
For I'm a-going away with a pretty little girl but I'm coming back again.

My Lindy is handsome. My Lindy, she's stout.
But she broke my new suspenders and she set down on my hat. CHORUS TWICE

I wish I was an alligator, that when I went to swim,
I'd open my mouth as wide as I could and I'd scoop my Lindy in. CHORUS 3 TIMES