What does the speaker have in common with the lamb and the lamb's creator?
From the poem, we can also see that the speaker and the lamb coexist peaceably within their creator's realm. The speaker uses his conversation with the lamb to convey a message that all of us have been given a place and role in this realm. With his innocent questioning, the speaker bids the lamb understand that he was created to "feed/ By the stream & o'er the mead" and to be dressed in "clothing of delight,/ Softest clothing wooly bright."
So, one thing the speaker has in common with the lamb and the lamb's creator is that all are participants in the reality that has been created on earth. The speaker asserts to the lamb that his creator is the Lamb himself. He draws a comparison between the innocent animal before him and the purity of his creator.
The biblical overtones suggest that the speaker has some knowledge about the story of Christian redemption and that he will use his voice to convey this message to the world. Both the young speaker and the animal are symbols of God's spotless character, and all three are united in a tripartite bond similar to that of the earthly trinity (Jesus, Mary, and Joseph) and the spiritual trinity (Jesus, the Father, and the Holy Spirit).
For he calls himself a Lamb:He is meek & he is mild,He became a little child:I a child & thou a lamb,We are called by his name.
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.