” Such as being informed that Satan (originally known as Lucifer before he was Satan) is the brother of the Lord Jesus Christ?”

A very true statement, it shows how we believe ongoing revelation and not just the hermeneutics of man.

Do you know that we also teach that you and every person on this earth is also a brother or a sister of our Lord Jesus Christ and his younger brother Lucifer?

A very true statement, it shows how we believe ongoing revelation and not just the hermeneutics of man.

Not just ongoing; but by repeating; too.

Sometimes Gods just have to repeat themselves...

...almost...

The Doctrine and Covenants

Section 15

Revelation given through Joseph Smith the Prophet to John Whitmer, at Fayette, New York, June 1829 (see the heading to section 14).

The message is intimately and impressively personal in that the Lord tells of what was known only to John Whitmer and Himself.

John Whitmer later became one of the Eight Witnesses to the Book of Mormon.

1–2, The Lord’s arm is over all the earth; 3–6, To preach the gospel and save souls is the thing of most worth.

1 Hearken, my servant John, and listen to the words of Jesus Christ, your Lord and your Redeemer.
2 For behold, I speak unto you with sharpness and with power, for mine arm is over all the earth.
3 And I will tell you that which no man knoweth save me and thee alone—
4 For many times you have desired of me to know that which would be of the most worth unto you.
5 Behold, blessed are you for this thing, and for speaking my words which I have given unto you according to my commandments.
6 And now, behold, I say unto you, that the thing which will be of the most worth unto you will be to declare repentance unto this people, that you may bring souls unto me, that you may rest with them in the kingdom of my Father. Amen.

Section 16

Revelation given through Joseph Smith the Prophet to Peter Whitmer Jr., at Fayette, New York, June 1829 (see the heading to section 14).

Peter Whitmer Jr. later became one of the Eight Witnesses to the Book of Mormon.

1–2, The Lord’s arm is over all the earth; 3–6, To preach the gospel and save souls is the thing of most worth.

1 Hearken, my servant Peter, and listen to the words of Jesus Christ, your Lord and your Redeemer.
2 For behold, I speak unto you with sharpness and with power, for mine arm is over all the earth.
3 And I will tell you that which no man knoweth save me and thee alone—
4 For many times you have desired of me to know that which would be of the most worth unto you.
5 Behold, blessed are you for this thing, and for speaking my words which I have given unto you according to my commandments.
6 And now, behold, I say unto you, that the thing which will be of the most worth unto you will be to declare repentance unto this people, that you may bring souls unto me, that you may rest with them in the kingdom of my Father. Amen.

The main difference between the Lord Jesus Christ and Satan is that Jesus is God, and Satan is a created being, an angel, called a cherub, a type of angel, which covered the throne of God.

They cannot be, and are not, brothers.

Satan (another name for Shatan/Adversary) has many names, of which one is SON OF THE MORNING. Another is Dragon, and Serpent.

Isaiah 14: 12-15:
“12 How art thou fallen from heaven, O Lucifer, son of the morning! how art thou cut down to the ground, which didst weaken the nations! 13 For thou hast said in thine heart, I will ascend into heaven, I will exalt my throne above the stars of God: I will sit also upon the mount of the congregation, in the sides of the north: 14 I will ascend above the heights of the clouds; I will be like the most High. 15 Yet thou shalt be brought down to hell, to the sides of the pit.”

Luke 10:17-19 (JESUS said:)
“17 ¶ And the seventy returned again with joy, saying, Lord, even the devils are subject unto us through thy name. 18 And he said unto them, I beheld Satan as lightning fall from heaven. 19 Behold, I give unto you power to tread on serpents and scorpions, and over all the power of the enemy: and nothing shall by any means hurt you. “

Revelation 12:9
“9 And the great dragon was cast out, that old serpent, called the Devil, and Satan, which deceiveth the whole world: he was cast out into the earth, and his angels were cast out with him.”

Lucifer was an angel. Jesus was/is the Word of God, who was with God and who IS/WAS God.

There is no way Lucifer and Jesus are brothers in any way - Jesus is of one being with the Father - the ineffable God, the incarnate Word and the Holy Spirit that is the love between these are ONE God, not multiple gods.