This lightsaber with a blue blade was the property of Darth Sidious, the Sith Master, following his return to life on Byss.
Darth Sidious maintained a collection of stolen lightsabers from the Jedi in his lab located on the Imperial throne-world, to be used if necessary; one of these lightsabers had a blue blade.
In 10 ABY, Luke Skywalker eliminated almost all of Sidious's clones. However, Sidious's spirit moved into the single remaining clone that Luke had not yet destroyed. This newly inhabited clone then seized his blue-bladed lightsaber from the lab wall and used it to duel Luke. Sidious was victorious in this fight, successfully turning Luke to the dark side and making him his apprentice.
Later, also in 10 ABY, Sidious discovered aboard his Super Star Destroyer, the Eclipse, that Luke had rejected the dark side due to the influence of his sister, Leia Organa Solo. Infuriated, Sidious attacked Luke with the blue-bladed lightsaber. Despite the immense power of the Sith Lord, Skywalker caught him by surprise. Shortly thereafter, the Eclipse was destroyed, taking with it Sidious's clone and his collection of stolen lightsabers.