The lore surrounding lightsabers and the Force-imbued crystals that power them are well-documented in both The Empire Strikes Back succeeded Star Wars, and Lucas’ original sequel story became the 1978 novel Splinter of the Mind's Eye, written by Alan Dean Foster. The book is now part of the Legends continuity, and one of its major plot elements was the Kaiburr crystal, an original iteration of a lightsaber crystal.
In both canon and Legends, lightsabers are powered by Force-connected crystals. In Legends, numerous varieties of lightsaber crystals can be found naturally in the galaxy, and crystals can also be synthesized using the Force or its dark side. Legends crystals glow in a specific color, determining the color of the lightsaber blade they’ll produce. In canon, there’s only one type of lightsaber crystal: Kyber crystals. Canon Kyber crystals can be found in Force-attuned parts of the galaxy, and they’re all initially clear. When a Kyber bonds with a Force , they change into a specific color. Dark side s cannot bond with a Kyber, so they torture them into submission, “bleeding” them and turning them red in the process.
In Splinter of the Mind’s Eye, Luke Skywalker and Leia Organa crash-land on Mimban, an Expansion Region world and the home of the legendary Kaiburr crystal, a powerful Force artifact that can heal the injured or sick, as well as significantly increase the strength of a Force (or dark side ). It isn’t long before Luke and Leia are at odds with Darth Vader, who seeks to capture them and the crystal. In the climactic finale, Luke and Leia both dueled Vader, with the Rebels only barely prevailing due to the Kaiburr empowering Luke and the spirit of Obi-Wan Kenobi guiding his actions. Luke and Leia would have died if not for the Kaiburr healing their injuries. Seeing as Lucas originally intended for the plot to be the focus of his sequel, the crystals would have been more or less a plot device, not a significant element showcased in canon.
In its initial appearance in Splinter of the Mind’s Eye, the Kaiburr crystal was largely used as a McGuffin with Luke and Leia escaping Mimban with it, and the artifact’s connection to lightsaber crystals was not delved into. The Legends-era lightsaber crystals and the canon continuity’s Kyber crystals were most likely inspired by the Force-enhanced gem from Splinter of the Mind’s Eye. Both continuities also feature numerous Force-imbued objects aside from crystals, such as Jedi and Sith Holocrons, the Legends-era Infant of Shaa, and the Nightbrother spear wielded by Savage Oppress in the canon timeline. Considering Lucas' franchise became immensely popular, there was an opportunity to adapt the lightsaber crystal into a more significant object rather than acting as a plot device.
In later Legends material, Luke and Leia learn that the Kaiburr crystal loses its power over time when away from the Temple of Pomojema on Mimban. Still, fragments of the Kaiburr could be used to power lightsabers like any other Force-imbued crystals. Decades after Splinter of the Mind’s Eye, Leia constructed a lightsaber using a fragment of the Kaiburr. Lumiya, the Sith successor to Darth Vader and Emperor Palpatine, acquired numerous fragments of the Kaiburr and constructed her signature weapon, a Sith lightwhip, with one of them. Thanks to the overwhelming success of Star Wars, Splinter of the Minds’ Eye became the first Expanded Universe novel, and George Lucas’ original iteration of the lightsaber crystal debuted with it.