Hi... yeah I usually sing "There was a Lad...." aka "Rantin Rovin' Robin" to the Dainty Davie tune.
The song as it stands is a bit much anyway, basically Burns is saying "what a crackin guy I am, sure I am?".. But the Dainty Davie tune does make it a bit gentler and more singable.
I just re-read your post and see what you were asking... the bouncy "Rantin Rovin Robin" tune was a later invention. The slower Dainty Davie air is the one to which he originally wrote "There was a lad...".
I'll see iof I can find out who wrote the newer tune for "There was a Lad"
Cheers
Steven