The lullaby Virgin Mary sang to the new born babe: not so sure....

That is the question!
Did she sing a lullaby in the cave of Bethleem to put baby Jesus to sleep?
When I remember all the Madonna paintings I have seen so far I cannot find one where she seems to sing by the cradle. I looked at the wiki page on 'Lullaby', the geographic area of Palestine is not mentionned. 
 If she did sing a lullaby like all mothers did in many cicilisations it woud have been some chant  without words to soothe the pains of birth for the baby and herself. That cradle song would be archaïc,  coming from the desert tradition of nomadic population.
I gazed at some paintings through internet, the 'most ancient ones' coming from the cave of Bethleem.
What is constant is that Mary does not move her lips and does not make the gesture to rock the cradle when there is a cradle, in most representations the baby is either in a manger or lying on  a white  diaper spread on straw.
So Imagination is the answer combined to the historital background of the Nativity, to think of the possibility of a lullaby for this amazing birth announced in the stars!
The tale of the three Wise Kings is such a wide open space for imagination !
Perhaps my ignorance in the music field does not help to find an ancient Palestinian lullaby.
What I found is a poem which is a  modern lullaby, the situation today has not changed much : it  deteriorated badly at the beginning of the month for the Palestinians.

 There is so much violence these days every where around us, violence towards young African male population on the roads of exile either through our Alps mountains not far from Nice or on our coasts not far from Italy, violence on our minds with the constant reminding of terrorism, that I simply need to dream about a quiet chant for a new born babe coming from another tradition which covers countries up to the Nile, the berber tradition.This is my Christmas carol so to speak, from Kabylie, another Berber family in North-Africa.