Just to muddy(cat) the waters, there's a recorded version by the New York State fiddler, Larry Older, [I don't care what the scholars in Oxford believe, a "fiddler" is someone who plays the violin and calls it a "fiddle"], which is much different from the syrupy tune you here in elevators. It begins:
Where are you going, I'm going to the fair
Flim limb a lea casa lo ma lea
If you see my love tell him I'll be there
To ma tassa a low, fa lass a low
Flim limb a lea casa low ma lea.

It's track A5 on "Adirondack Songs, Ballads and Fiddle Tunes."