The little that is known of Tyrius' history has been pieced together from different accounts throughout the RP. Much of it is only known by a select few people.
Tyrius was the firstborn son of Lord Gerion Lannister. Throughout his childhood, he and his brother, Loren Lannister, clamored for their father's attention, but received little. Tyrius became Lord of Casterly Rock and Warden of the West after his father's death. Loren became his right-hand-man, and Eddrick Lannett was his squire.
Just before the beginning of the Second Greyjoy Rebellion, Tyrius was sailing near Banefort when a storm sunk his ship. Drowned, his body was pulled from the sea by Gwynesse Greyjoy who revived him and brought him to her brother, Damron Greyjoy. Damron, already incensed over the slights of King Orys II Baratheon, took the Lannister for a spy and planned to have him executed in order to launch the Second Greyjoy Rebellion. Gwynesse however (who it is believed had fallen in love with Tyrius) convinced Alannys Greyjoy to help her free Tyrius. Alannys did so with the help of a drowned priest named Urron, who married them on the shores of Pyke after they escaped the dungeons.
With Tyrius gone, Damron launched the Second Greyjoy Rebellion, reaving and pillaging along the western coastline. Tyrius was able to arrive in time to trap the Ironborn host as it moved north after their loss at the Shield Islands, and destroyed most of their fleet during the Battle for Lannisport. It is unclear whether Tyrius joined the fight willingly or was forced to by his new king, Renly Baratheon, but he accompanied the King's forces during the Battle of Pyke where he died after receiving an axe wound to the arm. Shortly thereafter, Gwynesse gave birth to Tyrius' son Damon. She married Loren and together they claimed the child as his.
"Tyrius had a soft heart, gods rest his soul." - Jeyne Lannister
"A kind man that, impatient though, a trait that showed in his swordplay." - Ser Eddrick Lannett
"If it's an honourable death you want then go. Make yourself into an honourable corpse, Tyrius did. When he was dressed in his suit of gold and laid to rest in the crypts below Casterly Rock his honour was as much a use to him as it was when that axe took him in the arm." - Loren Lannister to Damon Lannister
“Honorable,” he said, but then corrected himself. “Foolhardy.” He kept his gaze trained on the parchment, and the name Damon rested his finger on. “Oftentimes the two are one and the same.” - Stafford Lannister describing Tyrius to Damon Lannister
“[Tyrius and Gwynesse] swore the vows as all must, beneath the moon, standing in the surf. He promised her that he would return. She wept like a child in his arms while he swore it over and over again. ‘I’ll come back, I’ll come back to you, I promise.’" - Urron
"[[[Loren Lannister|Loren]]] was a serious boy, true, but Tyrius wasn't and someone had to be." - Jeyne Estermont
Gerion Lannister, father (deceased)
Loren Lannister, brother (deceased)
Jeyne Lannister, sister
Damon Lannister, son