Since I don't always remember the words to real lullabies, I usually just make something up or modify a popular song (often from the 1980s).
I find that Tracy Chapman's "Baby Can I Hold You?" is very apropos (with small changes):
"Baby, can I hold you, tonight?I also often find myself singing this:
Maybe if I hold you the right away
Ooo, at the right time
You won't cry."
"Hey, little girl, is your daddy home...Maybe that one's weird.
Did he go and leave you all alone?
NO WAIT, I'M RIGHT HERE.
Ooh, ooh, ooh. I'm on fire."