In Leviticus, the priest is Aaron who puts the sin on the head of the scapegoat. In LOTR, it is Elrond who puts the ring on Frodo.

The entire purpose of the scapegoat is this Hebrew word: kpr. It has a dual meaning: deny/atone.

It is the same word used in the gospel, where Peter denies the Messiah three times, and therefore he must atone three times (John 21).

The Frodo/Gollum duality fulfill this purpose: Frodo atones while Gollum denies.

It is in the death of denial (kpr) that we learn to atone (kpr).

The day of kpr (Yom Kippur) is considered the holiest day of the year in the bible. This year (2022) it is celebrated on October 5. In Leviticus it was the one day that the head priest (Aaron) was allowed to enter the Holy of Holies in the tabernacle (a 15 foot cube room). Anyone else would die.

Remember when Elrond and Isildur entered Mt. Doom together. Isildur ended up dead (days later when the Ring slipped from his finger), but Elrond lived.

Mt. Doom is a picture of the corrupted temple. When Arda was first formed, Mt. Doom was likely beautiful and lush, probably with a name that preceded even Orodruin. But in later days, Mt. Doom was corrupted by the enemy. In the Hebrew bible, there are many passages that refer to the darkness that transpired in the temple. See e.g. Ezekiel.

Later, Sam and Frodo, followed by Gollum, enter Mt. Doom. Like priests themselves (remember they were commissioned by Elrond), the final test of faith is manifested, and Gollum falls.

Samwise fulfilled his duty to his friend, even carrying him up the mountain in the end. Frodo got as far as he could, he did the best he could. If Frodo had the inherent power to accomplish the mission without his darker side Gollum, it would have undermined the essential role of God (only God saves).

The journey of Frodo and Sam resonates with us today because we see in the story the essentialness of faith, and the works that result from faith. Each character was faithful to something, and the Lord over all worked it to good, and Aragorn was crowned king to begin the fourth age.