OK, for ya'll who love the so-called lullaby would want to watch this vid, cos you can download the music sheet! But the person playing it in the vid is the one who came up with it. Read the 'More info'.
This is what Carter Burwell noted on Bella's Lullaby on his website.
"Bella's Lullaby," as it appears in this film, was not written to be a lullaby but to speak of love - ecstatic, tormented love."