Well, in theory, it could. Fanfics often like to blend different fictional universes. However, in the official Harry Potter lore, there are no lightsabers. But in a fanfic, an author could come up with some creative magic or a cross - universe event that brings lightsabers into the wizarding world. Maybe a powerful wizard discovers a way to create a weapon similar to a lightsaber using magic and some rare materials.
He could find it during one of his missions. Maybe he's exploring an ancient ruin and stumbles upon the lightsaber. It could be in a chest or just lying there, and Naruto, being curious, picks it up.
Pikachu would probably be very curious. It might zap the lightsaber a bit to see what would happen, and then be in awe of the bright blade. It could also get a bit protective of Ash when he wields the lightsaber, as if it senses the added danger.
Perhaps it's given to him by a mysterious figure. This figure could be from another dimension or a very old ninja who has been in hiding for a long time. They recognize Naruto's potential and power, and decide that he is the one worthy of wielding the black lightsaber. This could be part of a bigger plan to help Naruto defeat a new and powerful enemy that neither the ninja world nor the normal means of combat can handle.
Naruto's fighting style would likely incorporate more acrobatic flips and spins to take advantage of the lightsaber's reach. He'd also use his shadow clone jutsu in new ways, like having clones surround an enemy while he attacks from above with the lightsaber.
Perhaps a lightsaber is discovered in a hidden part of Hogwarts, and it has some sort of ancient magic that is tied to the fate of the wizarding world. The characters then have to figure out how to use it, or how to keep it out of the wrong hands. They might also need to learn how it works, which could lead to some comical moments as they try to figure out things like how to turn it on and off, all while being chased by dark wizards who also want the lightsaber.
I think Hermione would be the most likely. She's very intelligent and a quick learner. She would study all the available information about lightsabers, probably find some ancient texts in the library about similar weapons. With her determination and knowledge - seeking nature, she'd be able to master the basic techniques of lightsaber handling in no time.
The black lightsaber has a unique and interesting story. It was created by Tarre Vizsla, the first Mandalorian to become a Jedi. It's a symbol of power and has passed through different hands over time, often being associated with important events in the Star Wars universe.
Another possibility is that the black lightsaber has some sort of special power or property that ties into the Naruto universe's existing powers. For instance, it could be attuned to chakra in some way. Maybe it can be powered by chakra instead of the typical energy source in the Star Wars universe. This would create an interesting dynamic as Naruto characters would have to learn how to manage this new form of power while still using their own ninja abilities.