Gunthor Lannister was a cousin to the main branch of House Lannister, and the eldest son of Stafford Lannister and Lady Olene Lannister. Jeyne Lannister once remarked that he is "stupid and slow" because Olene partook in drink while pregnant, but he is observed by many to be a knight of high caliber.
Gunthor was not among those of Olene's children who came to King's Landing for the Queen's feast.
He rode out to meet Damon Lannister at Deep Den when the King was returning to Casterly Rock, and escorted his party for the remainder of their journey. After Lord Byron Lannett made a scene at court over the sentencing of his son Walder Lannett (who King Damon ordered be gelded for rape), Ser Gunthor was sent to Payne Hall to bring Walder back to Casterly and ensure that Lord Lannett did not attempt to free his son from the castle by force.
Watching Gunthor spar outside the barracks of Casterly Rock, Ser Benfred Tanner observes that he is quite skilled.
At the Tournament of the Three Ships, Jeyne Estermont named Gunthor as her champion in a trial by combat against a peasant boy accused of kidnapping her daughter, Katelyn. On the verge of defeat, Ser Benfred Tanner killed Gunthor by playing to his honor and asking him to lift his visor before dealing the death blow. When Ser Gunthor obliged, Benfred threw a knife in his face.
"...it doesn’t matter how fine a child’s septa is, you can still be born stupid, and no maester can fix that. Look at Lady Olene’s oldest." - Jeyne Lannister
Ser Gunthor Lannister was walloping a man nearly twice his size, and making it look simple. - Blood and Whispers
“Ser Gunthor...has a spotless reputation and a good record.” - Lord Commander Ryman Sunglass
Stafford Lannister, father
Olene Lannister, mother
Tygett Lannister, brother
Maslyn Lannister, sister
Six other unnamed siblings