Peter, Paul and Mary did one that I’d always sing to kids in the hospital I think The name was Sing, Teddy All Day It was a tall tale with the last line being, “and he who tells a bigger tale, would have to tell a lie.”
I remember one little girl, about 4 years old I was rocking one night, every time I’d start that song she’d pat my mouth and say “DON’T SING!” :dubious:
That would be PP&M’s Autumn To May. Love that song, too! Brings back wonderful memories. 
Wow. I didn’t bother checking into this thread because I figured the most obvious oddball lullabye would already be mentioned. In fact, when I saw the thread title I assumed it was inspired by this lullabye, the oddball lullabye of oddball lullabyes:
Stay awake, don’t rest your head
Don’t lie down upon your bed
While the moon drifts through the skies
Stay awake, don’t close your eyes
Though the world is fast asleep
Though your pillow’s soft and deep
You’re not sleepy as you seem
Stay awake, don’t nod and dream
. . .
–“Stay Awake,” the anti-lullabye, from Mary Poppins.
Time to start that “wildly inappropriate lullabies” thread . . .
(And time to refresh my memory on the words to “Hurt.”)