The Lord Tywin is one of Cersei's dromonds in service to House Baratheon of King's Landing. It has twice as many oars as the King Robert's Hammer, the flagship of the royal fleet. It is named for Lord Tywin Lannister.
A Feast for Crows
The Lord Tywin is being built at the dockyards in King's Landing as part of Queen Cersei Lannister's plan to have a large fleet of powerful ships independent of the historic naval powers of the Iron Islands and the Arbor. It is the first of the new ships for the fleet to commence building. During her imprisonment by the Faith of the Seven, Cersei is visited by Qyburn, who tells the queen that Aurane Waters fled King's Landing with the new ships after her arrest.