It could be that he stumbles upon it during one of his quests. He's always getting into strange situations and finding unexpected things. He could be in a fight with some new and unknown monster, and in the chaos of the battle, the lightsaber just appears. Maybe it was dropped by a previous wielder who was fighting the same monster long ago and Percy is the one fated to pick it up and use it for good.
Well, he might find it in some mysterious place like an ancient temple. Maybe it was left there by a powerful being from another dimension.
Perhaps it was a gift from one of his godly parents or some other powerful entity in the Percy Jackson universe. They could have seen the potential in him having such a unique weapon and decided to bestow it upon him. This could also be part of a grander plan to help him in his future adventures against the forces of evil in both the Percy Jackson world and whatever new threats the lightsaber might attract from the Star Wars - inspired elements.
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.
Well, in this fanfiction, perhaps Percy could use his water - bending abilities to shape the kyber crystal. He might draw on his demigod skills to assemble the various parts of the lightsaber with precision. After all, he's used to handling weapons like Riptide, so adapting to building a lightsaber could be an interesting journey.
He probably has adventures fighting new and different kinds of monsters. The lightsaber would give him an edge in combat against creatures that are used to more traditional weapons.
In the fanfiction, Percy's lightsaber could be a sight to behold. The blade might be a shimmering silver - blue, reminiscent of the way moonlight reflects on water. The hilt could be made from a combination of materials - part celestial bronze, which is strong against monsters in his world, and part some sort of Jedi - inspired alloy. It could have small inscriptions in Ancient Greek that give it special powers, like the ability to cut through magical barriers as well as physical objects. And perhaps there would be a small compartment in the hilt where Percy could store a vial of water from a sacred spring, which he could use to boost the power of the lightsaber when needed.
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.
Well, in some fanfictions, Percy might obtain the spear as a gift from a minor god who sees his potential. For example, a god of an ancient and forgotten war cult could give it to him, seeing Percy as a worthy warrior to carry on their legacy.
In some fanfictions, he might find it in an ancient weapon stash hidden in a mythical location. Maybe while on a quest, he stumbles upon a secret chamber where the katana is kept as a powerful relic from an old civilization.
In some fanfictions, Percy might obtain the trident through a special quest. Maybe he has to prove himself worthy to an ancient sea deity who then bestows the trident upon him as a symbol of power and trust.
Perhaps he discovers it in an ancient, hidden temple dedicated to a forgotten god. The sword could be a gift from this god, who sees potential in Percy to use it for good.
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.