Mrrzy --

I absolutely agree.... Unless, maybe, you count the love song that resulted in the baby that needed the lullaby...

(...And this is the house that Jack built).

But the lullabies that are crooned by the cradle tend not to be recorded in formal notation until much later. Hymns, on the other hand, encode a nation's religious and/or political beliefs, and so get the honor of being pressed into clay tablets, and thus preserved for the ages.

On the other hand, since this music has no surviving lyrics, maybe it was a lullaby.