They're gonna go on epic adventures together! In the Legends timeline, because that's the best one, of course.

Vader was waking up after a lovely cat nap in a patch of sunlight, and he stretched out his back, quietly rumbling a soft purr of satisfaction. Golden rays of sunlight were beaming through the transparisteel window of Luke's Coruscant apartment, and the angle of the sun told him that it was late afternoon; he'd been asleep for a few hours.

He'd missed sunlight, during his years in the armor, and despite the glut of it available now, he always felt a bit of gratitude when the warmth of the sun touched upon his new body.

This was all very nice. Much nicer than he deserved, all told.

Except he was starting to get hungry, and Luke wasn't home yet. That wasn't nice at all, and in fact had the potential to become a disaster.

More at the link.

I blame this on @planningconquest with their Sabrina the Teenage Witch-esque AU where Vader is trapped in the form of the cat while his twins learn to be witches. 

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Piett was the last to leave the house. The investigation team stood next to the black car in the gravel driveway. He paused and looked back and saw Ms. Skywalker’s large cat sitting in the window. There was something unsettling about that cat, but for now, he put it out of his mind as he climbed into the driver’s seat of the car. 

“You think she was telling the truth?” Ozzel, Piett’s superior, asked. He sat in the front passenger seat adjusting the air vents so they blew directly on him. 

“I do,” Thrawn answered. “At least she answered our questions truthfully.” 

Ozzel twisted in his seat so he could look at the Indian man sitting in the back seat. “What do you mean by that?” 

“I mean, she picked her words very precisely,” Thrawn replied. 

“Think she’s hiding something?” 

“It’s possible she knows something in regards to her son, but I’m sure she is keeping it to herself to protect him.”

“Pah!” Ozzel said as he turned back around. “Protect him? Anakin Skywalker? She has it backwards. Skywalker doesn’t need to be protected. It’s everyone else we have to protect from Skywalker.” 

Piett sometimes wondered if that was true. He was the main point of contact with Shmi Skywalker. He called her every day to ask how she was doing and if she needed anything, and sometimes, he would drive out to her house and have coffee with her. Her cats would climb into his lap for pets as she talked warmly of her son. It was hard to believe she was talking about a mass murderer and terrorist. A man who was considered to be the most dangerous person on this planet. 

After a night on the town with the Rogues, Luke calls Father for a ride home - forgetting, apparently, that his formerly murderous Sith Lord of a father is currently for some reason a cat. The next morning, he gets to deal with the aftermath.

"Because as you know, Father is a sentient adult cat. And as you also know, because you drafted the laws on this, there's nothing in the laws of the New Republic that prevents him from obtaining citizenship. Or a driver's license. Because that would be discrimination. Speciesism of the worst sort."

"You," Leia began icily, "are deliberately muddying the waters - "

"I would never deliberately muddy the waters! I'm from Tatooine, water is a precious resource - "

" - and you are avoiding the central question, which is this: he might qualify for one, but does he actually have a driver's license to drive on Coruscant?"