Exodus 12

The Lord instructed Moses -

"Speak ye unto all the congregation of Israel, saying, In the tenth day of this month they shall take to them every man a lamb, according to the house of their fathers, a lamb for an house:
4 And if the household be too little for the lamb, let him and his neighbour next unto his house take it according to the number of the souls; every man according to his eating shall make your count for the lamb.
5 Your lamb shall be without blemish, a male of the first year: ye shall take it out from the sheep, or from the goats:
6 And ye shall keep it up until the fourteenth day of the same month: and the whole assembly of the congregation of Israel shall kill it in the evening.
7 And they shall take of the blood, and strike it on the two side posts and on the upper door post of the houses, wherein they shall eat it.
8 And they shall eat the flesh in that night, roast with fire, and unleavened bread; and with bitter herbs they shall eat it.
9 Eat not of it raw, nor sodden at all with water, but roast with fire; his head with his legs, and with the purtenance thereof.
10 And ye shall let nothing of it remain until the morning; and that which remaineth of it until the morning ye shall burn with fire."  (Old Testament | Exodus 12:3 - 10)

And -

"...thus shall ye eat it; with your loins girded, your shoes on your feet, and your staff in your hand; and ye shall eat it in haste: it is the LORD's passover.
12 For I will pass through the land of Egypt this night, and will smite all the firstborn in the land of Egypt, both man and beast; and against all the gods of Egypt I will execute judgment: I am the LORD.
13 And the blood shall be to you for a token upon the houses where ye are: and when I see the blood, I will pass over you, and the plague shall not be upon you to destroy you, when I smite the land of Egypt.
14 And this day shall be unto you for a memorial; and ye shall keep it a feast to the LORD throughout your generations; ye shall keep it a feast by an ordinance for ever."  (Old Testament | Exodus 12:11 - 14)

The Lord made it clear that this was a "token" and "ordinance" and was to be kept "for ever" or until He said it's purpose was fulfilled.  As one ponders the instructions of the Lord, you can see that it all points to the atonement of Jesus Christ for -

"...this is the whole meaning of the law, every whit pointing to that great and last sacrifice; and that great and last sacrifice will be the Son of God, yea, infinite and eternal."  (Book of Mormon | Alma 34:14)

 I believe the children of Israel understood this.  I could go through each point of these instructions to point out similarities, but rather, I will enter the comments of Elder Bruce R. McConkie -

“At the time appointed for their deliverance from Egyptian bondage, the Lord commanded each family in Israel to sacrifice a lamb, to sprinkle its blood on their doorposts, and then to eat unleavened bread for seven more days— all to symbolize the fact that the destroying angel would pass over the Israelites as he went forth slaying the firstborn in the families of all the Egyptians; and also to show that, in haste, Israel should go forth from slavery to freedom. As a pattern for all the Mosaic instructions yet to come, the details of the performances here involved were so arranged as to bear testimony both of Israel's deliverance and of her Deliverer. Among other procedures, the Lord commanded, as found in Exodus 12:

“1. ‘Your lamb shall be without blemish, a male of the first year,’ signifying that the Lamb of God, pure and perfect, without spot or blemish, in the prime of his life, as the Paschal Lamb, would be slain for the sins of the world.

“2. They were to take of the blood of the lamb and sprinkle it upon the doorposts of their houses, having this promise as a result: ‘And the blood shall be to you for a token upon the houses where ye are: and when I see the blood, I will pass over you, and the plague shall not be upon you to destroy you,’ signifying that the blood of Christ, which should fall as drops in Gethsemane and flow in a stream from a pierced side as he hung on the cross, would cleanse and save the faithful; and that, as those in Israel were saved temporally because the blood of a sacrificial lamb was sprinkled on the doorposts of their houses, so the faithful of all ages would wash their garments in the blood of the Eternal Lamb and from him receive an eternal salvation. And may we say that as the angel of death passed by the families of Israel because of their faith— as Paul said of Moses, ‘through faith he kept the passover, and the sprinkling of blood, lest he that destroyed the firstborn should touch them’ (Heb. 11: 28)— even so shall the Angel of Life give eternal life to all those who rely on the blood of the Lamb.

“3. As to the sacrifice of the lamb, the decree was, ‘Neither shall ye break a bone thereof,’ signifying that when the Lamb of God was sacrificed on the cross, though they broke the legs of the two thieves to induce death, yet they brake not the bones of the Crucified One ‘that the scripture should be fulfilled, A bone of him shall not be broken.’ (John 19: 31– 36.)

“4. As to the eating the flesh of the sacrificial lamb, the divine word was, ‘No uncircumcised person shall eat thereof,’ signifying that the blessings of the gospel are reserved for those who come into the fold of Israel, who join the Church, who carry their part of the burden in bearing off the kingdom; signifying also that those who eat his flesh and drink his blood, as he said, shall have eternal life and he will raise them up at the last day. (John 6: 54.)

“5. As ‘the Lord smote all the firstborn in the land of Egypt’ because they believed not the word of the Lord delivered to them by Moses and Aaron, even so should the Firstborn of the Father, who brings life to all who believe in his holy name, destroy worldly people at the last day, destroy all those who are in the Egypt of darkness, whose hearts are hardened as were those of Pharaoh and his minions.

“6. On the first and seventh days of the Feast of Unleavened Bread, the Israelites were commanded to hold holy convocations in which no work might be done except the preparation of their food. These were occasions for preaching and explaining and exhorting and testifying. We go sacrament meetings to be built up in faith and in testimony. Ancient Israel attended holy convocations for the same purposes. Knowing that all things operate by faith, would it be amiss to draw the conclusion that it is as easy for us to look to Christ and his spilt blood for eternal salvation as it was for them of old to look to the blood of the sacrificed lamb, sprinkled on doorposts, to give temporal salvation, when the angel of death swept through the land of Egypt?

“It was, of course, while Jesus and the Twelve were keeping the Feast of the Passover that our Lord instituted the ordinance of the sacrament, to serve essentially the same purposes served by the sacrifices of the preceding four millenniums. After that final Passover day and its attendant lifting up upon the cross of the true Paschal Lamb, the day for the proper celebration of the ancient feast ceased. After that Paul was able to say: ‘Christ our passover is sacrificed for us,’ and to give the natural exhortation that flowed therefrom: ‘Therefore let us keep the feast, not with old leaven, neither with the leaven of malice and wickedness; but with the unleavened bread of sincerity and truth.’ (1 Cor. 5: 7– 8.)” (The Promised Messiah, pages 429– 31)