Upon entering the ship, they find its AI is planning to reboot its systems and blow up the planet Han and Leia are currently galavanting across. Oh, and they find a ghost. The ship is being haunted by a Jedi named Callista who helps them fight the ship's malignant AI. Along the way, Callista and Luke fall in love.
In the process of destroying the ship, Luke's Padawan sacrifices herself. It's a hard day for Luke. He's got this new girlfriend who doesn't have a body and his new apprentice just got turned into a corpse. A ... hold on, you don't think Luke would ask his ghost girlfriend to ...? No. NO. Oh, come on, Luke. NO.
He does it. He lets his ghost girlfriend drive his apprentice's dead body. And she is good to go. She throws her undead parts at Luke repeatedly. She even surprises him by dressing his apprentice's corpse up in lingerie on their second anniversary, but Luke never goes all the way. However, the author does make it clear the two were very physical. They just always stopped short of fully switching off the targeting computer.