The lamb was to be roasted with fire not eaten raw or boiled. The lamb was to be proportioned between households so that everything would be eaten:
…every man shall take a lamb according to their fathers’ house, a lamb for a household. And if the household is too small for a lamb, then he and his nearest neighbor shall take according to the number of persons; according to what each can eat you shall make your count for the lamb. (Exodus 12:3-4 ESV)
It should have been eaten; yet the LORD made provision if it was not eaten:
And you shall let none of it remain until the morning; anything that remains until morning you shall burn. (Exodus 12:10 ESV)
At the first Passover the entire animal would have been consumed by fire, either by roasting and being eaten or by burning what was not eaten. Since boiling would not consume the uneaten portion, roasting ensured the entire animal would be consumed by a singular method of using fire.
At the first Passover blood was the most important element; without the blood on the doorposts and lintel a house was not passed over and the firstborn would have been killed. After the Passover the relationship between blood and meal changed: the meal becomes the most important element (blood was not a part of the service). Therefore the significance of roasting by fire should be seen in terms of the how this event would be commemorated in the future. In other words, the LORD’s instructions for the meal are purposeful in what the Israelites were to do on the first Passover to establish the foundation for how this event would be observed in the future.
The instructions on how and why this rite was to be observed in the future were given as part of the Passover:
You shall observe this rite as a statute for you and for your sons forever. And when you come to the land that the LORD will give you, as he promised, you shall keep this service. And when your children say to you, ‘What do you mean by this service?’ you shall say, ‘It is the sacrifice זֶֽבַח (zebah) of the LORD’S Passover, for he passed over the houses of the people of Israel in Egypt, when he struck the Egyptians but spared our houses.’”… (Exodus 12:24-27 ESV)
There is a significant connection with the history of the zebah offering and the Passover. The first zebah offering was made by Jacob on his return to the land promised to Abraham:
This heap is a witness, and the pillar is a witness, that I will not pass over this heap to you and this pillar to me, to do harm. The God of Abraham and the God of Nahor, the God of their father, judge between us.” So Jacob swore by the Fear of his father Isaac, and Jacob offered a sacrifice (zebah) in the hill country and called his kinsman to eat bread. They ate bread and spent the night in the hill country. (Genesis 31:52-54 ESV)
The second zebah offering was also made by Israel:
So Israel took his journey with all that he had and came to Beersheba, and offered sacrifices (zebah) to the God of his father Isaac. And God spoke to Israel in visions of the night and said, “Jacob, Jacob.” And he said, “Here I am.” Then he said. “I am God, the God of your father. Do not be afraid to go down to Egypt, for there I will make you into a great nation. I myself will go down with you to Egypt, and I will also bring you up again, and Joseph’s hand shall close your eyes.” (Genesis 49:1-4 ESV)
There is no mention of these sacrifices being made with fire. However that would be the most likely manner they would be made and it is unlikely they would have been made by boiling.
The third zebah offering was the sacrifice of the LORD’s Passover (Exodus 12:27). This means the zebah marks Israel’s entrance to and exit from Egypt. It also recalls the first zebah in Scripture made between Jacob and Laban when Jacob exited Paddan-aram and returned to Israel.
The meal is the centerpiece of the Passover service which was to declare that it was the sacrifice (zebah) of the LORD’S Passover to future generations:
”Passover was a family festival originally observed without reference to altar, sanctuary or priesthood (note the absence of ritual prescriptions in the Levitical calendar at Lev. 23:5)” 1
As commentaries note Leviticus has no instruction on the Passover sacrifice but it does identify the zebah sacrifice as the peace offering:
”If his offering is a sacrifice (zebah) of peace offering, if he offers an animal from the herd, male or female, he shall offer it without blemish before the LORD. (Leviticus 3:1 ESV)
The animal of the peace offering could be taken from either herds or the flocks and Chapter 3 describes how the sacrifice would be done for each of the different animals: one from the herd, a lamb, or a goat. Of the 3 the lamb offered had two unique aspects:
If he offers a lamb…(3:7)…the priest shall burn it on the altar as a food offering to the LORD. (Leviticus 3:11 ESV)
Only the lamb was specifically designated as a food offering to the LORD; the others were a “sweet savor to the LORD.” Only the lamb could be offered by the priest; the others were to be offered by Aaron and his sons. Thus the language and methods in Leviticus links the sacrifice (zebah) of the LORD’s Passover with the lamb offered as sacrifice (zebah) of the peace offering. The role of the priest when the lamb is sacrificed as a peace offering also parallels the first Passover where the father of each house (not only Aaron or his sons) selected and sacrificed the lamb.
Among the sacrifices described in Leviticus, boiling what is eaten separates the sin offering from all others:
…This is the law of the sin offering. In the place where the burnt offering is killed shall the sin offering be killed before the LORD; it is most holy. The priest who offers it for sin shall eat it… (6:25-26)… And the earthenware vessel in which it was boiled shall be broken… (Lev 8:28 ESV)
The language of Leviticus not only connects the sacrifice of the peace offering to the sacrifice of the LORD’s Passover, it differentiates that offering from the sin offering using the same method of cooking found in the Passover.
Roasting by fire establishes a physical connection with the meal of the zebah of the LORD’s Passover and the peace offering; not boiling continues that distinction to the sin offering. Therefore a Passover remembrance is also a reminder that the sacrifice made at Passover is a peace offering. It also remembers Israel’s entrance to and exit from Egypt and recalls the first zebah made between Jacob and Laban.
1. The International Bible Commentary p. 163