House Lannister
The richest house in the Seven Kingdoms, lords of Casterly Rock and the gold beneath it — stung in this age by Dagon Greyjoy's sack of Lannisport, which no amount of gold has yet avenged. Ser Tybolt Lannister rides as a champion at Ashford.
The fuller tale
Every great house keeps a founding story it half-believes; the Lannisters keep one that openly admits to being a con. Lann the Clever is said to have talked the old Casterly kings out of their own Rock rather than taking it by siege, and three thousand years later the house still prefers cleverness and coin to the blunter instruments other great houses reach for first.
The gold beneath Casterly Rock has made the Lannisters the wealthiest house in the Seven Kingdoms for longer than most families can trace their own lineages, and wealth of that scale buys a particular kind of pride — the sense that whatever else goes wrong, the west can always eventually purchase its way back to even.
That confidence took a real dent in this generation: Dagon Greyjoy's reavers sacked Lannisport itself, burned ships in the harbor of the richest house in the realm, and sailed home again before any western lord could muster a proper answer. It is the kind of insult gold cannot immediately undo, and the west's memory of it is, by every account, considerably longer than the time it has so far had to settle the account.
Representing the house on the Ashford tourney field is Ser Tybolt Lannister, riding as one of the era's notable champions and carrying, whether he says so aloud or not, a family that has not yet worked out how to answer Lannisport — a grievance quietly waiting for a westerman ruthless enough to actually collect on it.
The page and the screen
Ser Tybolt Lannister and the sack of Lannisport belong to background texture the novellas mention rather than scenes they stage, and neither has surfaced in the show's first season, which keeps its cameras on the Reach rather than the westerlands.