Doesn't, "Lay the Bent" mean aboput the same as, "Bend your elbow" or,"Get with it"? In which case it means, "Put some effort into sweeping the floor". Who knows? Maybe we're looking for something that isn't there.
What I'm getting at is that maybe some "minstrel" in the past had a cool sense of humor, and was kind of fed up with all the other nonsense lines found in celtic songs.

I used to have a dog named "Looie" who, when he was being energetic, looked for all the world like his pants were falling down. His mother's name was "Gussie. Well, on one long sailing adventure that my son David and I were on, we spent a lot of time laughing ourselves silly by making up "old Scottish Folk Songs" each verse of which ended with

AND YE' LOOIE PANTS A-FALLIN' DOON, AND AWA WI' YE' GUSSIE OH".
Could it be that, "Lay the bent to the bonny broom" followed by "Fa la la la fa la la la la la la" has it's roots in the same sort of sillyness?