Komentarz do Kapłańska 16:9

ועשהו חטאת means, when putting the lot upon it he names it (i.e. designates its purpose), using the words: "to the Lord as a sin offering״ (Yoma 39a).

ועשהו חטאת, the lot determines which of the male goats is to be the sin offering for the altar. In the words of our sages (Yuma 40) “the lot determines which is the sin offering, and not the name.” [calling it such is meaningless unless confirmed by the lot drawn. Ed.]

“A sin-offering.” I.e., “And do (offer) it as a sin-offering” means “he calls it a name... ‘a sin offering.’” You might ask: How does Rashi know this? Perhaps it means that he sacrifices it for the sake of a sin-offering, as is indeed the law of a sin-offering? The answer is: Later in the parsha (verse 15) it is written, “He shall slaughter the he-goat sin-offering,” which implies that he had not yet sacrificed it.

ועשהו חטאת, “and it will be made into a sin offering.” This was determined by lot. The High Priest had no hand in which of the two animals wound up as the sin offering.