The Lady Lumbridge is a ship named after the town of Lumbridge, and is involved in the Dragon Slayer quest. She is originally of Crandorian design, according to Klarense, but is damaged from "years of wear and tear".
However, they are attacked by Elvarg and, in a desperate effort to escape, run aground at Crandor, and the ship is severely damaged. With her hull ripped open, her base stuck in the sand, and her captain back in Draynor Village, she is no longer usable.
If the player somehow returns to the mainland after the ship crashes, the ship will return to the dock at Port Sarim. Klarense will remark that it seemed as if the tide magically brought the ship back to port. However, the ship will require another set of repairs. Ned will still be on board, but Jenkins will be dead.
It serves no purpose after the quest is complete, although players can take the planks left behind on the ground.
One thing to note is after the quest is complete, the player can talk to Klarense, and will ask Klarense about the ship. Klarense will respond that the ship behind him is a new ship that just looks like the Lady Lumbridge. According to the player, however, Lady Lumbridge is painted over somewhat, and replaced with "Klarense's Cruiser".