Soundly sleep, dreams are born in your slumber deep

My mum used to sing this to me, but I cannot find any reference to it anywhere... It puts my kids to sleep after a couple of minutes but I would love to know it's origins and if there's a second verse (a second verse would save me going bonkers repeating the same thing again and again!).

¿Caveman? Soundly sleep.
Dreams are born of your slumber deep.
When the dawn shall break,
You'll hear sounds that the birds shall make
Luh-luh-luh-luh-luh-lullaby
Luh-luh-luh-luh-luh-lullaby
Luh-luh-luh-luh-luh-lullaby
Luh-luh-luh-luh-luh-lullaby