I remember it from my childhood and have in my mind that it was recorded by Paul Robeson, who sang it at a street-corner meeting in Liverpool just after WW2.
I associate it with a chorus (probably a different song altogether) which goes:
Lula lula lula lula bye-bye'
Do you want the moon to play with,
Or the stars to run away with?
They'll come if you don't cry,
Lula lula lula lula bye-bye'
How your mammy's heart is aching;
But soon you'll be a sleeping lula,
Lula lula lula lula bye.
Jim Carroll