"Bang Away Lulu" is a traditional American song with many variations. It derives from older songs most commonly known as "Bang Bang Lulu", "Bang Bang Rosie" in Britain and "My Lula Gal" in the West. It was also used as a military cadence in both world wars. Most military cadences suggested explicit rhymes but skipped back to the chorus rather than complete them as in this version.
I learned it from "The New Lost City Bang Boys" (The New Lost City Ramblers) album Earth is Earth (1978).