Rom 14:11 For it is written, As I live, saith the Lord, every knee shall bow to me, and every tongue shall confess to God.
Every knee will eventually bow to Christ. There is a place prepared called 'outer darkness' and that is reserved for a Satan, his angels and a small handful of sons of perdition. We don't know what it is like there but I think they literally "perish".
From the appended article we learn that this is what is meant by "the mystery of godliness" not justification of the Trinity.
“For, behold, the mystery of godliness, how great is it! For, behold, I am endless, and the punishment which is given from my hand is endless punishment, for Endless is my name."
The Hell That Has No End
The three degrees of glory provide eternal homes for the vast majority of God’s children who merited earth life. There is a fourth destination, however, for those “comparatively few” who cannot abide even a telestial glory. The Lord explains that the destiny of the sons of perdition is a kingdom without glory (see D&C 88:24), and “the end thereof, neither the place thereof, nor their torment, no man knows,” only those “ordained unto this condemnation” (see D&C 76:43–49).
These are they who “cannot repent.” They “sin against the Holy Ghost” and “put Christ to open shame.” (See Joseph Fielding Smith, Doctrines of Salvation, comp. Bruce R. McConkie, 3 vols., Salt Lake City: Bookcraft, 1954–56, 1:47–49.)
All who partake of this, the greatest of sins, sell themselves as did Cain to Lucifer. They learn to hate the truth with an eternal hatred, and they learn to love wickedness. They reach a condition where they cannot repent. The spirit of murder fills their hearts and they would, if they had the power, crucify our Lord again, which they virtually do by fighting his work and seeking to destroy it and his prophets. …
Before a man can sink to this bitterness of soul, he must first know and understand the truth with a clearness of vision wherein there is no doubt. The Change of heart does not come all at once, but is due to transgression in some form, which continues to lurk in the soul without repentance, until the Holy Ghost withdraws, and then that man is left to spiritual darkness. Sin begets sin; the darkness grows until the love of truth turns to hatred, and the love of God is overcome by the wicked desire to destroy all that is just and true. In this way Christ is put to open shame, and blasphemy exalted.
How fortunate it is that in the mercy of God there will be comparatively few who will partake of this awful misery and eternal darkness.
Thus, hell has an end for all consigned to it except the sons of perdition. They alone remain in a hell which has no end.
https://www.lds.org/ensign/1986/04/i-have-a-question?lang=eng