Why did the priest cast lots on the two goats?
The priest cast lots on the two goats to see which goat would be killed and which would be left alive. The lots determined that one goat would be for the Lord, offered as a sin offering, and the other would be the scapegoat, presented alive before the Lord and then let go into the wilderness.
Les explains that the high priest started with three animals: a bullock for his own sacrifice and two kid goats. After using the bullock for himself and his family, he came to the two goats. He cast lots upon them—essentially drawing straws—to determine which goat would be killed and which would be left alive. One was designated for the Lord, the other for the scapegoat. The goat chosen by lot for the Lord was offered as a sin offering; its blood was taken behind the veil and sprinkled on the mercy seat. The scapegoat was presented alive before the Lord to make atonement and then let go into the wilderness. Les notes that the word 'scapegoat' is still used today for someone who takes the blame for another.
And he shall take the two goats, and present them before the LORD at the door of the tabernacle of the congregation.
And Aaron shall cast lots upon the two goats; one lot for the LORD, and the other lot for the scapegoat.