Summary
Unlike House Stark, House Mormont, House Tarly, and the Lannisters of Casterly Rock do not have a Valyrian steel sword at the beginning ofGame of Thrones. Per the events ofThrones, after the Northern army, led by Robb is decimated in the rebellion against the real power in Westeros - the Lannisters; Tywin reforges the ancestral House Stark Valyrian steel greatsword, Ice into two swords. These are subsequently named Widow’s Wail and Oathkeeper.
Tywin now asserts dominance as a political force inthe Seven Kingdoms, and two of the freshly reforged Valyrian steel blades served as symbols of his power and majesty. As he unveils the first of the two swords inGame of Thronesseason 4, episode 1 “Two Swords,” his son, Jaime Lannister remarks: “You’ve wanted one of these in the family for a long time.” Jaime’s words bring attention to the Lannisters' lost relic - the Valyrian steel greatsword - Brightroar that remained in possession of the House for a little more than a century from the time they acquired it. This raises the question of how the crafty Lannisters lost the Brightroar in the first place.

House Lannister Traded Gold For Brightroar
Monarchs from House Lannister bore the title of King of the Rock before the Targaryen Conquest, but after King Loren I Lannister bent the knee to Aegon I, he became Warden of the West and the first Lord of Casterly Rock. Because House Lannister ruled over the Westerlands, which was arguably the richest of kingdoms, it had the riches to acquire a Valyrian steel sword.Game of Throneslore states that Brightroar fell into the Lannisters' possession in the century that preceded the catastrophe known asthe Doom of Valyria. It was lost because a King of the Rock made a foolhardy attempt to sail into the ruins of Valyria. The lore states that the gold the Lannisters traded to acquire Brightroar was sufficient to build an army. Undoubtedly a symbol of glory, the monarchs from the House used Brightroar for combat purposes, until King Tommen II fool’s errand trying to bring home the treasures of ruined Valyria.
What Happened To Brightroar
The Valyrian Peninsula was home to ancient peoples, including the forty powerful noble families, the finest smiths, and mages. The civilization suffered a collapse due to a volcanic cataclysm - an event known inGame of Throneslore as the Doom of Valyria. Interestingly, the erstwhile rulingHouse Targaryen of Westerostraces its roots to Old Valyria and was the dragon-riding family that survived this cataclysm because it escaped well before time.
King of Casterly Rock - Tommen II Lannister carried Brightroar with him to doomed Valyria. He sailed into the ruins with the intention of pillaging the treasures that he believed would be left behind from its heyday. Both King Tommen II and Brightroar vanished in this fateful journey. Years later, Tywin Lannister’s youngest brother - an impetuous person named Gerion journeyed to Valyria with the intention of recovering House Lannister’sancestral Valyrian steel sword, but like his ancestor, he was never to be seen again. Gerion’s nephew and Tywin’s youngest, Tyrion wanted to accompany him on the quest but was forbidden from doing so. Tywin made an attempt to bring back his brother by sending a search party for him, but Gerion’s last known whereabouts were traced to Volantis.Game of Throneslore says that Volantis is where Gerion’s crew deserted him because he intended to sail into the Smoking Sea. He had to buy slaves to make up for half of his crew.

Two Valyrian Steel Swords In The Family
Reforging Ice was Tywin’s last resort, as no one, including himself could have predicted the outcome of the so-called the War of the Five Kings. He’d tried in vain to acquire a replacement sword from the poorernoble Houses in the realm. None of the Houses would trade their heirlooms with Tywin because swords and other combat weapons are valuable commodities in the world ofGame of Thrones.
As such, Tywin was proud to have obtained two swords from Ice, but tragically only one of those came in aid of House Lannister.Joffrey never used Widow’s Wail, but Jaime wielded it inGame of Thronesseason 7 to fight the Dothraki horde while coming back from Highgarden to King’s Landing. He also slayed countless Wights in the Battle of Winterfell with his Valyrian steel sword, as did Brienne with her blade, Oathkeeper.

As for the Lannisters' ancestral Valyrian steel greatsword, Brightroar,the House held on to itfor a little more than a hundred years. Its disappearance is an unresolved mystery inGame of Throneslore.