Here are just some of the many, many ways that Christ fulfilled the role of the Passover lamb.
For even Christ our passover is sacrificed for us: Therefore let us keep the feast... [1 Corinthians 5:7-8]
1. The Jews call the Passover, "the festival of redemption". [The Jewish Festivals; by Hayyim Schauss]
Christ is our Redeemer [Galations 3:13, Titus 2:13-14, and many more].
2. The Passover lamb had to be killed at 3 pm on the first month of the holy calendar (14th day of Nissan).
Christ died at 3 pm on the first month of the holy calendar. (Matthew 27:45-50)
3. The Passover lamb had to be killed in Jerusalem, but outside of the city gates. (Deuteronomy 16:5-6, then look at 2 Kings 21:4)
Christ was killed in Jerusalem, but outside of the city gates. (John 19:16-19, Hebrews 13:10-13)
4. The Passover lamb must be unblemished. (Exodus 12:5)
Christ was unblemished (1 Peter 1:18-20)
Also, when Pilate said, "I find no fault in him." [John 19:4, 6] he was essentially saying, that Christ was without blemish.
5. The whole assembly shall kill the Passover lamb. (Exodus 12:6)
Everyone who has ever sinned [which means everyone] is responsible for killing Christ.
6. Not a bone on the Passover lamb was to be broken.[Exodus 12:46]
Not a bone on Christ was broken.[John 19:33-36]
7. The Jews would put their name on their lamb
God put His name on His Lamb!. (This is real cool!)
8. In preparation of the Passover, the Jews would go through their house in search for leaven (leaven represents sin [Matthew 16:6-12, Luke 12:1, 1 Corinthians 5:2-8]) and clean all the leaven from their house.
In Matthew 21:1-13, you can see that Jesus went into Jerusalem, then cast out the thieves from the temple. So, that would mean that at the same time the Jews were cleaning the leaven from their houses, God was cleaning the leaven (sin) from His house.
9. The last words from the high priest as he cut the Passover lamb's throat was "It is finished" [The Seven Festivals of the Messiah; by Eddie Chumney]
"When Jesus therefore had received the vinegar, he said, 'It is finished': and he bowed his head, and gave up the ghost." [John 19:30]
That means that at the same time that the high priest was saying "It is finished" (referring to the Passover sacrifice), The High Priest (Jesus) was saying the exact words (referring to The Passover sacrifice)!
10. "In Jesus' day, vinegar was soured wine, plain and unmixed, This was given to Jesus when He said, "I thirst!" (John 19:28-30) This was simultaneously spoken by the high priest on the temple mount." [The Passion What does it Mean; by Dr. Bree Keyton]
11. "The highest point in the evolution of the Pesach (Passover) came in the last century of the second Temple, when the Jews suffered from the heavy oppression of the Romans. It was during this period that the Messianic hope flamed up, and in the minds of the Jews the deliverance of the future became bound up with the first redemption in Jewish history: the deliverance from Egypt...This belief gained added strength in this period of Roman occupation and oppression. Jews began to believe that the Messiah would be a second Moses and would free the Jews the self-same eve, the eve of Pesach (Passover). So Pesach (Passover) became the festival of the second as well as the first redemption;... Jewish hearts beat faster on the eve of Pesach (Passover), beat with the hope that this night the Jews would be freed from bondage of Rome, just as their ancestors were released from Egyptian slavery." [The Jewish Festivals; by Hayyim Schauss]
The really awesome thing is that at the same time when the Jews were looking so hard for the Messiah to bring the second redemption on Passover eve, the Messiah did bring the second redemption on Passover eve!
12. The blood of the Passover lamb was put on the doorposts for death to pass over their houses.
When we accept God's perfect sacrifice for our sins, we enter into God's family. By faith, we walk though the doorway into God's house, through the blood of The Lamb (Christ) that is on the doorposts, and death will pass over us!
There is much more on this topic. Here are a couple of very good books about this topic.