The LORD who dealt with ancient Israel is the member of the God Family who became Jesus Christ (I Corinthians 10:1-4). Therefore this goat, which was sacrificed for a sin offering and whose blood was sprinkled on the mercy seat for an atonement for all Israel, represented Jesus Christ.
Although the two goats appeared to be alike, one was to typify Christ. Men were utterly unqualified to determine which goat was suitable. Therefore it was necessary for God to decide.
Casting a lot is a solemn appeal to God to decide a matter supernaturally (Proverbs 16:33). It is a sacred religious ceremony. Modern lotteries profane this ancient holy ceremony appealing to God.
Men, without God's supernatural intervention, are unable to determine who represents Christ. Many people who think they worship Christ are actually following ministers who are deceived by the Devil (II Corinthians 11:13-15). Satan has so deceived the whole world (Revelation 12:9) that mankind as a whole does not know who is God and who is the adversary.