One of the versions had a second verse:

I hear the lark, the lark hears me
down through the leaves of the old oak tree,
Please let the lark that sings to me,
sing to the one I love.

Refrain...

I see now that there are many versions, some seem to have evolved like the game of telephone, but I seem to recall something very elemental from the images in the song. The oak tree is supposed to represent life, and wisdom, being passed from the parent singing to the child being rocked to sleep.