Relevant verses:
Leviticus 16:7-10 7 Then he shall take the two goats and set them before the Lord at the entrance of the tent of meeting. 8 And Aaron shall cast lots over the two goats, one lot for the Lord and the other lot for Azazel. 9 And Aaron shall present the goat on which the lot fell for the Lord and use it as a sin offering, 10 but the goat on which the lot fell for Azazel shall be presented alive before the Lord to make atonement over it, that it may be sent away into the wilderness to Azazel.
Leviticus 16:15-16 15 “Then he shall kill the goat of the sin offering that is for the people and bring its blood inside the veil and do with its blood as he did with the blood of the bull, sprinkling it over the mercy seat and in front of the mercy seat. 16 Thus he shall make atonement for the Holy Place, because of the uncleannesses of the people of Israel and because of their transgressions, all their sins. And so he shall do for the tent of meeting, which dwells with them in the midst of their uncleannesses.
Leviticus 16:20-22 20 “And when he has made an end of atoning for the Holy Place and the tent of meeting and the altar, he shall present the live goat. 21 And Aaron shall lay both his hands on the head of the live goat, and confess over it all the iniquities of the people of Israel, and all their transgressions, all their sins. And he shall put them on the head of the goat and send it away into the wilderness by the hand of a man who is in readiness. 22 The goat shall bear all their iniquities on itself to a remote area, and he shall let the goat go free in the wilderness.
Question: Are the lot cast for the two goats meant to communicate that they are interchangeable and thus are really the same goat or the same sacrifice whose complex function can only practically be expressed through the role played by two different goats?
In other words, is the casting of the lots meant to tie together the two outcomes, the purification of the Holy Place from the transgressions/uncleanness of the people of Israel and the carrying of their sins far away, so that we are to understand that the sacrifice of the one actually accomplishes both the temple purification and the mass carrying away of sins?