In William Blake's Songs of Innocence and Experience, the poet connects the lamb, the child, and Christ through symbolism. Let's look at some examples of this.
In “Introduction,” the speaker meets a mysterious child who is sitting on a cloud. The child laughs and tells the speaker, “Pipe a song about a Lamb!” The child then weeps at the song. The symbolism is heavy here. The song is presumably about the lamb, Christ, the lamb of God (see John 1:29), and as such, it is both sorrowful and joyful, for Jesus died on the cross to atone for human sin and opened the gates of heaven. The lamb, an image that comes from the Old Testament Passover and sacrificial rituals, is a symbol of Christ.
We might wonder, too, about the identity of the child. The child asks for a song and then weeps. This child clearly knows the story well and is affected by it. We may reflect that perhaps the child also represents, or even is, Christ, asking the speaker to tell His own story, not so much for His benefit as for the speaker's. He continues to weep, partly for joy and partly, perhaps, for those who have not yet heard the song.
The poem “The Lamb” also blends the images of lamb, child, and Christ. The speaker is a child, filled with wonder and innocence. He speaks to a little lamb, asking the animal if it knows who made him. The Creator, the speaker says, “calls Himself a Lamb.” He even “became a little child” like the speaker. They are both, child and lamb, called by His name. He is the ultimate lamb, the ultimate child, from whom all others lambs and children receive their characteristics, especially their innocence.
All three, lamb, child, and Christ, are images of innocence. Christ is the perfect image, of course, for He is the sinless one, God incarnate, and lambs and children in their own innocence point to Him and model this trait to the world.
Blake also uses lambs and children to symbolize joy, as he does in “The Little Black Boy” when he speaks of the lambs rejoicing and God's children rejoicing around His tent. The lamb can also represent peace, for in “Night,” the speaker lies down beside a lamb and sleeps in peace, thinking of “Him who bore thy name.”