(just did the google-fu)... If Millie Small did that song, I can’t find any mention of it. Only of the Rosanne Cash version.
Full title of Rush’s Barney Frank update theme is “My Boy Lollipop”. There is another song called “Lollipop”, a quasi-novelty record done by the Chordettes.
https://www.youtube.com/watch?v=3rYoRaxgOE0
I had no idea that Roseanne Cash touched either of those songs. I can’t picture it, though I will check them out.