In order to understand the LDS doctrine regarding Lucifer one must also understand its doctrine of man. The LDS Church teaches that everyone, Jesus and Lucifer included, had a pre-mortal existence where we were born as spirit children of God and his wife. In the LDS teaching manual Gospel Principles we read:
God is not only our ruler and creator; he is also our Heavenly Father. . . . Every person who was ever born on earth was our spirit brother or sister in heaven. The first spirit born to our heavenly parents was Jesus Christ (see D&C 93:21), so he is literally our elder brother (see Discourses of Brigham Young, p. 26). Because we are the spiritual children of our heavenly parents, we have inherited the potential to develop their divine qualities. (Gospel Principles, 1997, p. 11 [link])
However, prior to this spirit birth each of us had eternally existed as an "intelligence." Angels, devils, mortals and gods are regarded as the same species but in different stages of advancement or judgment. In one of Joseph Smith's revelations we read, "Man was also in the beginning with God. Intelligence, or the light of truth, was not created or made, neither indeed can be" (Doctrine and Covenants 93:29). According to another of Smith's revelations, God told Abraham:
I dwell in the midst of them all . . . for I rule in the heavens above, and in the earth beneath, in all wisdom and prudence, over all the intelligences thine eyes have seen from the beginning; I came down in the beginning in the midst of all the intelligences thou hast seen.
Now the Lord had shown unto me, Abraham, the intelligences that were organized before the world was; and among all these there were many of the noble and great ones. (Abraham 3:21-22, Pearl of Great Price)
According to LDS doctrine, the two oldest sons of God were Jesus and Lucifer. Lucifer convinced one-third of his brothers and sisters to join him in rebellion and were expelled from Heaven (see Gospel Principles, chapter 3 [link]). The other two-thirds became the humans born on our earth. This doctrine is mainly drawn from Joseph Smith's revelations in the Book of Abraham and the Book of Moses in the Pearl of Great Price. According to Joseph Smith, Moses recorded:
And I, the Lord God, spake unto Moses, saying: That Satan, whom thou hast commanded in the name of mine Only Begotten, is the same which was from the beginning, and he came before me, saying—Behold, here am I, send me, I will be thy son, and I will redeem all mankind, that one soul shall not be lost, and surely I will do it; wherefore give me thine honor.
But, behold, my Beloved Son, which was my Beloved and Chosen from the beginning, said unto me—Father, thy will be done, and the glory be thine forever.
Wherefore, because that Satan rebelled against me, and sought to destroy the agency of man, which I, the Lord God, had given him, and also, that I should give unto him mine own power; by the power of mine Only Begotten, I caused that he should be cast down;
And he became Satan, yea, even the devil, the father of all lies, to deceive and to blind men, and to lead them captive at his will, even as many as would not hearken unto my voice. (Moses 4:1-4, Pearl of Great Price)
This is discussed in the current LDS Sunday School manual for children ages 8-11:
This doctrine was further explained in the June 1986 LDS magazine Ensign. The question was asked "How can Jesus and Lucifer be spirit brothers when their characters and purposes are so utterly opposed?" Jess L. Christensen, Institute of Religion director at Utah State University, Logan, Utah, responded:
On first hearing, the doctrine that Lucifer and our Lord, Jesus Christ, are brothers may seem surprising to some — especially to those unacquainted with latter-day revelations. But both the scriptures and the prophets affirm that Jesus Christ and Lucifer are indeed offspring of our Heavenly Father and, therefore, spirit brothers. Jesus Christ was with the Father from the beginning. Lucifer, too, was an angel who was in authority in the presence of God, a son of the morning. (See Isa. 14:12; D&C 76:25-27.) Both Jesus and Lucifer were strong leaders with great knowledge and influence. But as the Firstborn of the Father, Jesus was Lucifer's older brother. (See Col. 1:15; D&C 93:21.)
How could two such great spirits become so totally opposite? The answer lies in the principle of agency, which has existed from all eternity. (See D&C 93:30-31.) Of Lucifer, the scripture says that because of rebellion he became Satan, yea, even the devil, the father of all lies. (Moses 4:4.) Note that he was not created evil, but became Satan by his own choice.
When our Father in Heaven presented his plan of salvation, Jesus sustained the plan and his part in it, giving the glory to God, to whom it properly belonged. Lucifer, on the other hand, sought power, honor, and glory only for himself. (See Isa. 14:13-14; Moses 4:1-2.) When his modification of the Fathers plan was rejected, he rebelled against God and was subsequently cast out of heaven with those who had sided with him. (See Rev. 12:7-9; D&C 29:36-37.)
That brothers would make dramatically different choices is not unusual. It has happened time and again, as the scriptures attest: Cain chose to serve Satan; Abel chose to serve God. (See Moses 5:16-18.) . . .
We can only imagine the sorrow of our Heavenly Father as he watched a loved son incite and lead a rebellion and lose his opportunity for exaltation. But we can also imagine the Fathers love and rejoicing as he welcomed back the beloved son who had valiantly and perfectly fought the battles of life and brought about the great Atonement through his suffering and death. ("I Have a Question," Ensign, June 1986, p. 25-26 [link])
Apostle John A. Widtsoe explained:
The story of Lucifer is the most terrible example of such apostasy. ... He pitted his own plan and will against the purposes of God. He strove to gain the birthright of his Elder Brother, Jesus the Christ. When his proposition was rejected, he forsook all that he had gained, .... He was no longer Lucifer, bearer of truth, who walked in light, but Satan, teacher of untruth, who slunk in darkness. He became the enemy of God and of all who try to walk according to the Lord's commandments. One-third of the spirits present in that vast assembly supported Satan and became enemies of the truth that they had formerly cherished. With him these rebellious spirits lost their fellowship with the valiant sons of God. (Evidences and Reconciliations, p. 209)
Apostle Bruce R. McConkie stated:
God lives in the family unit. He is our Father in heaven—the literal and personal Father of the spirits of all men. He begat us; we are the offspring of Heavenly Parents: we have an Eternal Father and an Eternal Mother. We were born as spirits, and we dwelt in the presence of our Eternal Parents; we lived before our mortal birth. As spirits we were in all respects as we are now save only that we were not housed in mortal bodies as is the present circumstance. Christ was the Firstborn of all the heavenly host; Lucifer was a son of the morning: each of us came into being as conscious identities in our appointed order; and Christ is our Elder Brother. (The Mortal Messiah, vol. 1, p. 21)
President Spencer W. Kimball commented on the relationship of Lucifer to Jesus:
The importance of not accommodating temptation in the least degree is underlined by the Savior's example. Did not he recognize the danger when he was on the mountain with his fallen brother, Lucifer, being sorely tempted by that master tempter? He could have opened the door and flirted with danger by saying, "All right, Satan, I'll listen to your proposition. I need not succumb, I need not yield, I need not accept—but I'll listen." (The Teachings of Spencer W. Kimball, p. 163)
President Spencer W. Kimball also wrote:
Similarly Satan had contended for the subservience of Moses. Satan, also a son of God, had rebelled and had been cast out of heaven and not permitted an earthly body as had his brother Jehovah. Much depended upon the outcome of this spectacular duel. Could Lucifer control and dominate this prophet Moses, who had learned so much directly from his Lord? (Faith Precedes the Miracle, p. 87)
Apostle George Q. Cannon taught:
The adversary ... aims to destroy us. Angry that his plan was not adopted in the heavens; angry at his failure in the rebellion against God and at his expulsion from the courts of glory; angry at his being deprived of a body, he and those who fell with him have been eager ever since that dreadful time to destroy their brethren and sisters who did not rebel with them. We who are here tonight, as well as all who are upon the earth, kept our first estate. We did not listen to Lucifer. He was a mighty angel; he had exceedingly great power in the presence of God. He used his great influence with the family of God to convince them that the plan which he proposed was the better one, and to persuade them to reject the plan of God and his Son Jesus, our elder brother. Failing in this, he has, apparently, declared war against all his brethren and sisters who were honorable and maintained their allegiance to God. Therefore he is continually spreading snares for the feet of the children of men. (Collected Discourses, edited by Brian Stuy, vol. 1, May 19th, 1889, p. 255)
In 1949 Apostle Joseph F. Merrill stated:
Now there is another personality of which I desire to speak, ... that person is Satan, the Devil. But according to our understanding and teaching, Satan is a person with a spirit body, in form like that of all other men. He is a spirit brother of ours and of our Lord Jesus Christ, who is our Elder Brother in the spirit world. The earth was in course of development for the abode of man in mortality. A Redeemer was to be sent down and make it possible for the Father's children to return to him. (LDS Conference Report, April 1949, p. 27)
Speaking in 1857, Apostle Joseph Young taught:
Who is it that is at the head of this? It is the Devil, the mighty Lucifer, the great prince of the angels, and the brother of Jesus. He left the province of his Father, and took with him a third part of his Father's kingdom, and there was no other alternative but to banish him. God would have saved him if he could; but he could not. (Journal of Discourses, vol. 6, pp. 207-208, October 11, 1857)
In 1844 LDS author W. W. Phelps wrote:
And again, we exclaim, O Mormonism! No wonder that Lucifer, son of the morning, the next heir to Jesus Christ, our eldest brother, should fight so hard against his brethren; he lost the glory, the honor, power, and dominion of a God and the knowledge, spirit, authority and keys of the priesthood of the son of God!
Christ kept his first estate—Lucifer lost his by offering to save men in their sins on the honor of a God, or on his father's honor.—Christ hated sin, and loved righteousness, therefore he was anointed with holy oil in heaven, and crowned in the midst of brothers and sisters, while his mother stood with approving virtue, and smiled upon a Son that kept the faith as the heir of all things. (Times and Seasons, vol. 5, p. 758, Jan. 1, 1844, art. by W. W. Phelps)
However, the Bible never presents Lucifer as the brother of Jesus. Angels were a separate creation from man.
Nehemiah 9:6—Thou, even thou, art LORD alone; thou hast made heaven, the heaven of heavens, with all their host, the earth, and all things that are therein, the seas, and all that is therein, and thou preservest them all; and the host of heaven worshippeth thee.
The first chapter of Hebrews shows that Jesus is the creator, not a created angel:
Hebrews 1:2—[God] Hath in these last days spoken unto us by his Son, whom he hath appointed heir of all things, by whom also he made the worlds;...
Hebrews 1:4-5—[Jesus] Being made so much better than the angels, as he hath by inheritance obtained a more excellent name than they. For unto which of the angels said he at any time, Thou art my Son, this day have I begotten thee? And again, I will be to him a Father, and he shall be to me a Son?
At the end of the world Satan and the rest of the fallen angels will be cast down to hell:
Jude 1:6—And the angels which kept not their first estate, but left their own habitation, he hath reserved in everlasting chains under darkness unto the judgment of the great day.
In 2 Peter 2:4 we read:
... God spared not the angels that sinned, but cast them down to hell, and delivered them into chains of darkness, to be reserved unto judgment;
Below is a quote from Nelson's New Illustrated Bible Dictionary:
DEVIL
(accuser)—the main title for the fallen angelic being who is the supreme enemy of God and man. Satan is his name, and devil is what he is—the accuser or deceiver. The title "devil" appears 35 times in the NKJV. In every case it is preceded by the article "the," indicating a title rather than a name. The term comes from a Greek word that means "a false witness" or "malicious accuser."
Several descriptive phrases applied to the devil in the New Testament point out the nature of his wicked personality and the extent of his evil deeds.
That Serpent of Old (Rev. 12:9; 20:2). The devil worked through the serpent to tempt Eve (Gen. 3:1-6).
The Wicked or Evil One (Matt. 6:13; 13:19,38; 1 John 2:13). This phrase depicts the devil's fundamental nature. He is in direct opposition to everything God is or all he wishes to do. ...
Enemy (Matt. 13:25,28,39). The devil is man's worst enemy. ... He is an enemy of Christ, the church, and the gospel; and he is tireless in his efforts to uproot good and sow evil.
Murderer (John 8:44). "He was a murderer from the beginning" are strong words from the lips of Jesus. The devil killed Abel and the prophets, and he wanted to kill Jesus before His time (8:40).
Deceiver (Rev. 20:10). Starting with Eve, the devil has attempted to deceive every living soul. Evil men operating under the power of the evil one will continue to deceive (2 Tim. 3:13).
Beelzebub, the Ruler of the Demons (Matt. 9:34; 12:24). Beelzebub (see also 2 Kin. 1:2-3, 6, 16) means literally "lord of Flies" and is a title of ridicule. The religious leaders of Jesus' time were guilty of blasphemy against the Holy Spirit because they claimed the miracles of Jesus were actually conducted by the devil. ... There are many demons but only one devil. His name is Beelzebub, the chief leader of the fallen angels known as demons.
...
Ruler of This World (John 12:31; 14:30; 16:11). Three times Jesus called the devil the "ruler of this world." The devil offered the world to Jesus if He would worship him (Luke 4:5-7), but the Lord refused with these words, "Get behind me Satan" (4:8). At Calvary God dealt a death blow to this world ruler. It is only a matter of time before God will win the final victory at the end of time (1 John 3:8; Matt. 25:41; Rev. 12:7). (Nelson's New Illustrated Bible Dictionary, 1995, Thomas Nelson Pub.)
For further information on this topic see:
[off site link] On Mike Huckabee's Question:
"Is the Mormon Jesus the Brother of Satan?"