But it is a deliberate distortion. They teach that “we all” are brothers.
No distortion. Jesus and Lucifer were two brothers vying against one another to be the Redeemer so all of us other spirit children of the Mormon god could potentially become gods too. That isn’t a distortion. That’s the sad reality of Mormon doctrine.
Specifically, they teach that God the Father is a spiritual and physical being who created a large number of spirit beings in Heaven, all of whom were his sons and daughters.
One son was named Jehovah, another son was named Michael and another son was named Lucifer. There were many other sons besides.
Jehovah volunteered to help the Father redeem his future creation of mankind and the Father accepted the offer. Jehovah's brother Lucifer was jealous of this new status given to another brother instead of himself and went to war against his brother and his father.
Michael was the leader of Jehovah's other brothers who came to Jehovah's aid against Lucifer.
As a reward, Michael the spirit being became the soul of the first man, Adam and Jehovah the spirit being became the soul of the redeemer, Jesus. The spirit being Lucifer was cast down into Hell and became Satan.
This is LDS teaching on the matter.
Of course, this kind of theological discussion has no place in a presidential election.