Each of the three types of people Nephi has described will receive the same end. By not being able to follow the true way of God, they are necessarily following the false way of Satan, and will share in his fate. They stand before God, and are righteously judge according to their works. In the case of each of the examples, the particular “works” are those things which did prevented them from repenting and following God. The specific terminology of death and hell echo the terminology and concepts Jacob expounds in his discussion of the nature of death and hell in 2 Nephi 9:10-12.
2 Nephi 9:10-12
10 O how great the goodness of our God, who prepareth a way for our escape from the grasp of this awful monster; yea, that monster, death and hell, which I call the death of the body, and also the death of the spirit.
11 And because of the way of deliverance of our God, the Holy One of Israel, this death, of which I have spoken, which is the temporal, shall deliver up its dead; which death is the grave.
12 And this death of which I have spoken, which is the spiritual death, shall deliver up its dead; which spiritual death is hell; wherefore, death and hell must deliver up their dead, and hell must deliver up its captive spirits, and the grave must deliver up its captive bodies, and the bodies and the spirits of men will be restored one to the other; and it is by the power of the resurrection of the Holy One of Israel.
The final judgement for these people condemns them to “the place prepared for them, even a lake of fire and brimstone, which is endless torment.” The Lord explains some important information about this “endless torment” in the Doctrine and Covenants:
D&C 19:4-12
4 And surely every man must repent or suffer, for I, God, am endless.
5 Wherefore, I revoke not the judgments which I shall pass, but woes shall go forth, weeping, wailing and gnashing of teeth, yea, to those who are found on my left hand.
6 Nevertheless, it is not written that there shall be no end to this torment, but it is written endless torment.
7 Again, it is written eternal damnation; wherefore it is more express than other scriptures, that it might work upon the hearts of the children of men, altogether for my name’s glory.
8 Wherefore, I will explain unto you this mystery, for it is meet unto you to know even as mine apostles.
9 I speak unto you that are chosen in this thing, even as one, that you may enter into my rest.
10 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. Wherefore—
11 Eternal punishment is God’s punishment.
12 Endless punishment is God’s punishment.
In the very particular case of “endless torment,” the Lord explains that this is a terminology that is applicable to his punishment because he is the issuer of such a punishment to those who earn it.
Similarly, the “lake of fire and brimstone” is a metaphor that is best known for its modern application than its scriptural roots. In the Old Testament (using the KJV for the correlation to the terminology) fire and brimstone are a means God uses to deal with the wicked. In the specific case of Sodom and Gomorrah, we find:
Gen. 19:24
24 Then the LORD rained upon Sodom and upon Gomorrah brimstone and fire from the LORD out of heaven;
The wicked of Sodom and Gomorrah receive punishment from the Lord, and that punishment is in fire and brimstone. This same concept becomes universalized as God’s mode of punishment of the earthly wicked in Psalms:
Ps. 11:5-7
5 The LORD trieth the righteous: but the wicked and him that loveth violence his soul hateth.
6 Upon the wicked he shall rain snares, fire and brimstone, and an horrible tempest: this shall be the portion of their cup.
7 For the righteous LORD loveth righteousness; his countenance doth behold the upright.
From the Old Testament’s usage of the concept for the wrath of God we arrive at John’s use in Revelations, where the wrath of God is not that directed upon the earth-bound wicked, but rather on the post-judgement wicked in the next life. The image is the same, but the context is transformed from the earth to the afterlife.
Rev. 14:9-11
9 And the third angel followed them, saying with a loud voice, If any man worship the beast and his image, and receive his mark in his forehead, or in his hand,
10 The same shall drink of the wine of the wrath of God, which is poured out without mixture into the cup of his indignation; and he shall be tormented with fire and brimstone in the presence of the holy angels, and in the presence of the Lamb:
11 And the smoke of their torment ascendeth up for ever and ever: and they have no rest day nor night, who worship the beast and his image, and whosoever receiveth the mark of his name.
This is the eternal fate of the wicked who “worship the beast,” or those who follow Satan. Satan himself shall receive the same treatment:
Rev. 19:20
20 And the beast was taken, and with him the false prophet that wrought miracles before him, with which he deceived them that had received the mark of the beast, and them that worshipped his image. These both were cast alive into a lake of fire burning with brimstone.
Rev. 20:10
10 And the devil that deceived them was cast into the lake of fire and brimstone, where the beast and the false prophet are, and shall be tormented day and night for ever and ever.
Certainly the “lake of fire and brimstone” was an image and vocabulary item quite familiar to Joseph Smith, dating to usage in John. The use of the image in Nephi is more consistent with John’s image than with the Old Testament not only in vocabulary, but in the realm to which the punishment is assigned. It is precisely because this punishment pertains to the afterlife that it may be judged “endless.” This also fits well with John’s pronouncement in Revelations 14:11, that “the smoke of their torment ascendeth up for ever and ever.”
Nevertheless, while the particular phrase “lake of fire and brimstone” is certainly attributable to the King James Version of Revelations, it was also sufficiently part of the common vocabulary of the time to have entered Joseph’s vocabulary though common usage. The Old Testament/New Testament division is likewise not a dramatic division, but rather an application of the terminology to the post-judgement existence. Since Nephi’s context is also clearly the afterlife, the use of the imagery of God’s justice in that location is only a very slight shift from the Old Testament usage.