The lineage of House Lannister can be traced back to the great warrior Tywin Lannister. He was and is considered as one of the most formidable and thought-provoking Lords of Inmortalis. Tywin Lannister was present in the beginning of Lanier's reign, he saw the boy's potential but also Lanier's eventual downfall. He once tried to persuade Lanier away from his delinquent activities in order to focus on politics and rightful etiquettes of a good King, but Lanier was not one to obey or follow instructions.
However, when it came to the time where Lanier marched to the East to defeat the Rule of Titans, Tywin Lannister marched beside him and led his army to partake in the destruction of the Titans and their eventual extinction. Tywin was recorded to have helped kill Olympus and rescue Serafina Girelon beside Lanier Leonhart. After his great service to Lanier, he was given nobility and lordship of his name and thus the birth of House Lannister.
It wasn't long after his road to nobility did Tywin gain another advantage to his fingertips. Lanier called him once more to become his Hand of the King, which Tywin greatly accepted. By this time Tywin had already fathered three children: Cersei, Jaime and Tyrion Lannister with his wife Joanna Lannister.
Cersei and Jaime were known as the Lions of Casterly Rock, known for their unbelievable good looks. However, Tyrion or most commonly dubbed as 'The Imp' became Tywin's subject of embarrassment. Nevertheless, his faithful and loving wife loved all their children equally and Tywin soon accepted the faith of his youngest son. After the great feast that happened in Casterly Rock, however, no one has dared to call Tyrion Lannister as 'The Imp' anymore, not to his face and neither when he's turned back. It was rumoured that Tywin Lannister silenced all of those who dared to speak ill against Tyrion, cutting off their tongues in return.
