Which lamb in the Old Testament is Jesus equated to?
St. John the Evangelist notes St. John the Baptist’s testimony about Jesus in his Gospel (Jn 1:29) as the Lamb of God: ”The next day, John saw Jesus coming to him, and he saith: Behold the Lamb of God, behold him who taketh away the sin of the world.”
Jesus is called the lamb of God because he is the perfect sacrifice offered to God. In 1 Peter 1:18-19 we are told, “You were ransomed . . . not with perishable things like silver or gold but with the precious blood of Christ as of a spotless unblemished lamb.” A prophecy about the Messiah states, “Though he was harshly treated, he submitted and opened not his mouth; Like a lamb led to the slaughter” (Isaiah 53:7). After Jesus' crucifixion, soldiers did not break his legs to kill him because he was already dead. Like the Passover lamb, his bones were unbroken.
Even St. Paul, one of the pillars of Rome states, “Our paschal lamb, Christ, has been sacrificed” (1 Corinthians 5:7). Jesus' death on the cross was a passover from death to life for himself and for all of us. By his blood we are saved from death. Jesus made it possible for us to break out of the slavery of sin and death. He gave us the hope of reaching our promised land, heaven. The Gospel of John clearly compares Jesus to the Passover lamb by saying that Jesus was crucified the same day that the Passover lambs were being killed in the Temple (John 19:31).
Get rid of the old yeast, so that you may be a new unleavened batch—as you really are. For Christ, our Passover lamb, has been sacrificed. -
1 Corinthians 5:7
The Catholic Encyclopedia affirms this symbolism.
The whole of the lamb must be consumed — head, feet, and entrails — and if any thing remain of it until morning it must be burned with fire. The Israelites are commanded to eat the meal in haste, with girded loins, shoes on their feet, and staves in their hands "for it is the Phase (that is, Passage) of the Lord." The blood of the lamb on the doorposts served as a sign of immunity or protection against the destroying hand of the Lord, who smote in one night all the first-born in the land of Egypt, both man and beast. This ordinance is repeated in abridged form in Numbers 19:11-12, and again in Deuteronomy, xvi, 2-6, where sheep and oxen are mentioned instead of the lamb.
That the Paschal Lamb prefigured symbolically Christ, "the Lamb of God", who redeemed the world by the shedding of His blood, and particularly the Eucharistic banquet, or new Passover, has always remained the constant belief of Christian tradition. - Paschal Lamb
The Catholic Encyclopedia goes on to explain elsewhere the symbolism of the Lamb in Catholic thought and tradition. Not all symbolism is understood in the same way, even amongst theologians. The Lamb of is most unique an Christ being our Paschal Lamb, the the Lamb symbolism as used within Catholicism is far reaching and diverse. Sorry if this goes a little of subject, but it is quite interesting.
The Lamb (in Early Christian Symbolism)
Another cycle of catacomb paintings (not numerous) represents a lamb, or a sheep, with a milk-pail either on its back or suspended from a pastoral staff. A unique fresco of this order shows a shepherd milking a sheep, while still another shows milk-pail on an altar between two sheep. The frescoes of this type (of the sheep and milk-pail) were, until recently, generally regarded as symbols of the Eucharist, but Mgr. Wilpert dissents from the received opinion, and regards all frescoes in which allusions to milk occur as symbolic of the joys of Heaven. Both the earlier and the later interpretations depend on a well-known text of the Acts of Sts. Perpetua and Felicitas. While in prison awaiting martyrdom, St. Perpetua tells us she beheld in a vision an immense garden, and in the centre thereof the tall and venerable figure of an old man in the dress of a shepherd, milking a sheep. Raising his head, he looked at me and said, 'Welcome, my daughter.' And he called me to him and he gave me of the milk. I received it with joined hands and partook of it. And all those standing around cried ' Amen'. And at the sound of the voice I awoke, tasting an indescribable sweetness in my mouth." The community of ideas between this description and the catacomb frescoes of the sheep and milk-pail is so apparent that, at first view, the current interpretations of this class of representations would seem to be obviously accurate. Wilpert, however, calls attention to the fact that the things described in the vision of St. Perpetua took place not on earth, but in heaven, where the Eucharist is no longer received . Hence he regards the frescoes of the milk-pail class as symbolic of the joys which the soul of the deceased possess in paradise.
The lamb, or sheep, symbol, then, of the first class described, has, in all catacomb paintings and on sarcophagi of the fourth century, always a meaning associated with the condition of the deceased after death. But in the new era ushered in by Constantine the Great the lamb appears in the art of the basilicas with an entirely new signification. The general scheme of apsidal mosaic decoration in the basilicas that everywhere sprang into existence after the conversion of Constantine, conformed in the main to that described by St. Paulinus as existing in the Basilica of St. Felix at Nola. "The Trinity gleams in its full mystery", the saint tells us. "Christ is represented in the form of a lamb; the voice of the Father thunders from heaven; and through the dove the Holy Spirit is poured out. The Cross is encompassed by a circle of light as by a crown. The crown of this crown are the apostles themselves, who are represented by a choir of doves. The Divine unity of the Trinity is summarized in Christ. The Trinity has at the same time Its own emblems; God is represented by the paternal voice, and by the Spirit; the Cross and the Lamb denote the Holy Victim. The purple background and the palms indicate royalty and triumph. Upon the rock he stands Who is the Rock of the Church, from which flow the four murmuring springs, the Evangelists, living rivers of Christ" (St. Paulinus, "Ep. xxxii, ad Severum", sect. 10, P.L. LXI, 336). The Divine Lamb was usually represented in apsidal mosaics standing on the mystic mount whence flow the four streams of Paradise symbolizing the Evangelists; twelve sheep six on either side, were further represented, coming from the cities of Jerusalem and Bethlehem (indicated by small houses at the extremities of the scenes) and proceeding towards the lamb. The lower zone, no longer in existence, of the famous fourth-century mosaic in the church of St. Pudenziana, Rome, originally represented the lamb on the mountain and probably also the twelve sheep; the existing sixth-century apse mosaic of Sts. Cosmas and Damian at Rome gives a good idea of the manner in which this subject was represented.
According to the "Liber Pontificalis", Constantine the Great presented to the Lateran baptistery, which he founded, a golden statue of a lamb pouring water which was placed between two silver statues of Christ and St. John the Baptist; the Baptist is represented holding a scroll inscribed with the words: "Ecce Agnus Dei, ecce qui tollit peccata mundi." From the fifth century the head of the lamb began to be encircled by the nimbus. Several monuments also show the lamb with its head surmounted by various forms of the Cross; one monument discovered by de Vogüé in Central Syria shows the lamb with the Cross on its back.
The next step in the development of this idea of associating the Cross with the lamb was depicted in a sixth-century mosaic of the Vatican Basilica which represented the lamb standing on a throne, at the foot of a Cross studded with gems. From the pierced side of this lamb, blood flowed into a chalice whence again it issued in five streams, thus recalling Christ's five wounds. Finally, another sixth-century monument, now forming part of the ciborium of St. Mark's, Venice, presents a crucifixion scene with the two thieves nailed to the cross, while Christ is represented as a lamb, standing erect at the junction of the crossbeams. One of the most interesting monument showing the Divine Lamb in various characters is the sarcophagus of Junius Bassus (d. 358).
Two other scenes show a lamb receiving the Tables of the Law on Mount Sinai and striking a rock whence issues a stream of water. Thus in this series, the lamb is a symbol, not only of Christ, but also of Moses, the Baptist, and the Three Children in the fiery furnace. The fresco the cemetery of Praetextatus, showing Susanna as a lamb between two wolves (the elders), is another example of the lamb as symbol of one of the ordinary faithful.
To make things clear, I think you misrepresent Christ being prefigured in Leviticus 16. Sheep are not goats. Sheep and goats are closely related: both are in the subfamily Caprinae. However, they are separate species, so hybrids rarely occur and are always infertile.
4 He shall be vested with a linen tunick, he shall cover his nakedness with linen breeches: he shall be girded with a linen girdle, and he shall put a linen mitre upon his head: for these are holy vestments: all which he shall put on, after he is washed.
5 And he shall receive from the whole multitude of the children of Israel two buck goats for sin, and one ram for a holocaust.
6 And when he hath offered the calf and prayed for himself, and for his own house,
7 He shall make the two buck goats to stand before the Lord in the door of the tabernacle of the testimony:
8 And casting lots upon them both, one to be offered to the Lord, and the other to be the emissary goat:
9 That whose lot fell to be offered to the Lord, he shall offer for sin:
10 But that whose lot was to be the emissary goat, he shall present alive before the Lord, that he may pour out prayers upon him, and let him go into the wilderness. - Leviticus 16 4-10
In the 11th century, the Christology of Saint Anselm of Canterbury specifically disassociates the Lamb of God from the Old Testament concept of a scapegoat, which is subjected to punishment for the sins of others without knowing it or willing it. Anselm emphasized that as Lamb of God, Jesus chose to suffer in Calvary as a sign of his full obedience to the will of the Father. Simply confer this read: The Christology of Anselm of Canterbury