In the books Edit
In the A Song of Ice and Fire novels Lady Forlorn is currently in the possession of Ser Lyn Corbray, the eldest brother of Lord Lyonel Corbray, having inherited it for taking it in the Battle of the Trident after their father, then the Lord Corbray, had been wounded and using it to slay Prince Lewyn Martell. Lyonel still resents not having inherited the blade even though he inherited all family titles and lands.
The name "Lady Forlorn" is actually a legacy from the Andal invasion and predates the Valyrian steel blade. King Robar II Royce claimed the original Lady Forlorn after slaying Qyle Corbray, King of the Fingers. Robar wielded this Lady Forlorn during the Battle of the Seven Stars, using it to kill Torgold Tollett and a decoy dressed as Ser Artys Arryn. The Corbrays claim that Ser Jaime Corbray slew Robar in the battle, allowing them to reclaim the original Lady Forlorn.