Joybell and others,

There's no lady with an alligator purse in these examples that I'm going to re-post, but I think there are still relevant to this thread.

I believe that the rhyme your American husband remembers or a similar rhyme is probably the prototype for not only the children's rhyme "Miss Lucy Had A Baby", but also the large family of children's handclap rhymes known as "Miss Susie [or some other female name] Had A Steamboat" [or "Tugboat"].

I hope that it's alright for me to re-post this example of the
"Bang Away On Lulu" rhyme from the early days of Mudcat:

Subject: RE: Naughty kids'greatest hits
From: Downeast Bob - PM
Date: 01 Oct 97 - 05:19 PM

The way I knew it in the 50s, was:
Lulu had a steamboat; steamboat had a bell; Lulu went to heaven; steamboat went to

Bang away on Lulu, bang away all day. Who you gonna bang on when Lulu's gone away?

Lulu had a chicken; she also had a duck; She put them on the table to see if they would

Bang away on Lulu, bang away all day. Who you gonna bang on when Lulu's gone away?

Lulu spilled her orange juice, Lulu broke her glass; Then she slipped upon it and broke her little

Bang away on Lulu, bang away all day. Who you gonna bang on when Lulu's gone away?

Ask me no more questions; I'll tell you no more lies; Lulu got hit with a bucket of shit, right between the eyes!"

-snip-

Compare that with this example of the "Miss Susie Had A Steamboat" rhyme:

MISS SUZIE HAD A STEAMBOAT
lol i member Miss Suzie when i use to play hand games. here mine and my friends version

Miss Suzie had a steamboat the streamboat had a bell. Miss Suzie went to heaven.The steamboat went to----Hello operater give me number nine,And if you disconnect me Ill cut off your behind the fridgerater there was a peice of glass. Miss Suzie sat upon it and broke her little--Ask me no more questions. Tell me no more lies. The boys are in the bathroom. Zipping up their flies Are in the meadow the bees are in the park. Miss Suzie and her boyfriend are kissing in the d-a-r-k d-a-r-k d-a-r-k DARK DARK DARK. I know i know my ma. i know i know my pa. I know i know my sister with a 40 acre bra. My mom gave me a nickle.My dad gave me a dime. My sister gave me her boyfriend. He kissed me all the time. My mom took back her nickle. My dad took back his dime. My sister took back her boyfriend and gave me Frankenstien. I kicked him over China, I kicked over France.I kicked to Hawaii where he learn the hula dance OI!
        
http://blog.oftheoctopuses.com/000518.php; posted by XxBloodyRosexX
at February 11, 2005 [used with permission from that blog's members]

-snip-

Both "Bang Away On Lulu" {or some such name} and "Miss Susie Had A Steamboat" are profanity avoidance rhymes, though the "bad" words {as some children refer to them}at the end of one line are suggested by the first word in the next line. The children's version of
"Miss Lucy Had A Baby" doesn't have that profanity avoidance feature. However, there are some risque versions of that rhyme as demonstrated by this example from another Mudcat thread:

Subject: RE: Heigh Ho, Heigh Ho, I Bit the Teacher's Toe!
From: GUEST,Caro - PM
Date: 24 Mar 05 - 09:45 AM

This variation was sung by Alan Breeze (ye gods, how old am i?) on the Billy Cotton Band Show - Sunday lunchtimes.

Lulu had a baby - she called him Sonny Jim
She put him in the bathtub to teach him how to swim
He swam down to the bottom and then up to the top
Lulu got excited and grabbed him by his ...
Haircut, shampoo, ring the barbers bell
And if he doesn't like it
Just tell him, what the!
hey there! say there!
How's about a kiss?
Hey there! say there!
That's the end of this.

-snip-

Btw, I started a thread for "Ask Me No Questions" Rhymes, except I misspelled the word "no". That thread is thread.cfm?threadid=90284