Earlier in this discussion Sorcha provided a link to a Google Question & Answer thread. That thread included examples of "Bang Bang Lulu" and other rhymes. As a result of that discussion, I looked for and found several threads about several of those rhymes that have the title "More Work For The Undertaker". And the more I read examples of those rhymes, the more I think that some of their verses of this rhyme are related to "Bang Bang Lulu". I also believe that more directly through the "Bang Bang Lulu" rhyme, versions of "More Work For The Undertaker" are related to at least two children's playground rhymes- "Miss Susie Had A Steamboat" and "Miss Lucy Had A Baby".

I posted the examples from that discussion of "More Work For The Undertaker" on this Mudcat thread:
thread.cfm?threadid=21520&messages=29
Lyr Req: More Work for the Undertaker

I hope that some folks reading this "Bang Bang Lulu" thread will also read that "More Work For The Undertaker" thread and see what you think about the similarities between those two rhymes,as well as the similarities between "More Work For The Undertaker {MWFTU} and the "Miss Susie/Steamboat" and "Miss Lucy/Baby" rhymes.

In my next post to this thread I'll posts a few verses that seem to me to show a common source between "More Work For The Undertaker {MWFTU} and the "Miss Susie/Steamboat" and "Miss Lucy/Baby" rhymes.
I think that source began with either "MWFTU" and/or "My Lulu Gal" {or some such older version of "Bang Bang Lulu"} and then later became core parts of the "Miss Susie/Steamboat" and "Miss Lucy/Baby" and probably several other contemporary children's handclap or skipping {jump rope} rhymes.