What does the speaker have in common with the lamb and the lamb's creator?

Little Lamb, I'll tell thee, 
Little Lamb, I'll
tell thee. 
He is called by thy name, 
For He calls Himself a
Lamb. 
He is meek, and He is mild; 
He became a little
child. 
I a child, and thou a lamb, 
We are called by His
name.

These lines from
William Blake's poem, The Lamb contain the answer to your question.
The speaker who addresses the lamb in the poem is a child, a human child, endowed with
the gift of language, whereas the addresse, a lamb, is a non-human child, a dumb child.
In these lines the speaker explores in his simple language of childhood innocence how
the creator of the lamb who is also the creator of the child is both a child and a lamb.
Christ Himself was referred to as "the Lamb of God", and the creator was born in the
form of a human child: the babe in the manger. The creator is
"meek" and "mild", and the speaker does have these features of "meekness" and 'mildness"
in common with the lamb and its creator.