DARK SOULS III - Lorian, Elder Prince and Lothric, Younger Prince bossfight

Lothric and Lorian (along with Ocelotte) are the sons of King Oceiros and the queen of Lothric (possibly Gwynevere), they are said to be inseparable due to a curse, when the bell tolled to signify the fading of the flame, they rejected their duty to become Lords of Cinder and watched the fire fade from a distance.

Lothric may have never actually become a Lord of Cinder despite having a throne dedicated to him in Firelink Shrine; he wasn't resurrected nor did he abandon his throne like the other Lords, he never took his throne in the first place. There are several points in the game that confirm this:

They are not mentioned in the opening cutscene.
The description of their soul implies they never became Lords of Cinder.
Lothric still has his sanity, something that most dead/hollow and resurrected beings in the Dark Souls universe lack, suggesting he never died.
After returning all Cinders of a Lord to their thrones, Lothric's head is the only one that still has its flesh.
The only counter-argument to this theory is the "Lord of Cinder Fallen" message upon their defeat, but that might be because he was destined to be one.

Note: There is a theory that the royal family of Lothric wanted to create the perfect Heir to the Fire but failed, which is why Lothric is cursed.