Redemption of Sin

Jesus was referred to in the Bible as God's lamb (John 1:29). The lamb was not mentioned for the atonement of sins; rather, it was mentioned only as a sacrificial animal at the Passover.

Commentaries are your friend for Jn 1:29 e.g.

29 For the note of time see the commentary on verses 19–28. “Coming” will here mean “approaching,” not “coming to him for the first time.” Verses 26 and 32–33 show that John had recognized Jesus as the Christ on an earlier occasion. “Look” is a favorite expression in this Gospel, and John uses it more often than all the other New Testament writers put together.43 The expression “the Lamb of God” has passed into the general Christian vocabulary. But for all that it is very difficult to know exactly what it means. It is not found elsewhere in the New Testament (though Jesus is sometimes spoken of as “the Lamb,” especially in Revelation45), nor in any previous writing known to us. Thus we are not able to appeal to some other writing as John’s source. The genitive “of God” may mean “provided by God” (cf. Gen. 22:8), or “belonging to God.” Perhaps in his usual manner the Evangelist wants us to combine both meanings. But to what does “the Lamb” refer? Many suggestions have been made, among which we notice the following: (i) The Passover Lamb, a suggestion supported by the apparent identification of Jesus’ sacrifice with the Passover in 19:36. Against it are two main points, the one that the Passover victim was not necessarily a lamb at all, and the other that the proper term in use at the time for the Passover victim was not “lamb” but “Passover” (pascha). Another objection, that the Passover was not an expiatory sacrifice (and thus could not be said to take away the world’s sin), is not valid. All sacrifice was held to be expiatory,50 and, specifically, the Passover was sometimes viewed in this way. (ii) The lamb “led … to the slaughter” (Isa. 53:7). This is possible, but nothing in the context points to it. We can hold this view only if we can feel that there was such a widespread acceptance of the view that Isaiah 53 applied to the Messiah that an unexplained reference to a lamb and to the taking away of sin would be seen to refer to that chapter. That Christians in due course came to understand the chapter in this way is clear enough. That those who heard John the Baptist did so is not. This explanation of the words is unlikely.

Morris, L. (1995). The Gospel according to John (pp. 126–128). (NICNT Jn)

IIRC Jonathan Edwards has written on this from a typological perspective ... sorry but I don't know the title.