From Digitrad:

LYDIA, THE TATTOED LADY
(E.Y. Harburg)
@tattoo
filename[ LYDTATOO

yes the Muppet Silly Songs CD has this on it and darn them for it. I was a Nanny in Graduate School 2 days a week and my small charge made me sing that drat song every night or he refused to go abed.

That same CD has "I'm my own Grandpa" not exactly a child's song!

It also has a weird little ditty about worms that the kiddies alwyas love.

I hear that Tape in my dreams sometimes, I played it so often to calm my charge down. He was 2 and a half when his Lydia obsession began. He's now about age 20. I wonder if his girlfriend has tattoos?

Having no children of my own, it's amazing to consider how much Lullabye and silly song time I've put in rocking cousins and charges to sleep or to coax them to eat their broth or porridge. More than most mothers of three I'd wager.