☁History

Ⓗistory
This is a Direct Copy and Paste from Diseny’s Wiki page

☁Kingdom Hearts Novels
Larxene was discovered by Xigbar and became the twelfth member of Organization XIII, as well as the only female member. Shortly after joining, she found Axel and engaged in a conversation with him. She asked him how she looked in her new outfit, and when he did not produce a response, she took it as a sign that he found her unsatisfying to talk to. Axel explained that he was simply confused as to why she started talking to him for no reason, and that it wasn't that he found her presence unappealing, he simply found it "nothing". After a moment of silence, Larxene quietly complained that the castle was boring, and then bid goodbye to a still-confused Axel.
Some time later, she met another new member, Marluxia, with whom she is well-acquainted at this point. After asking him how he arrived at the Organization, the two neophytes agreed that the castle was boring. The discussion soon shifted to their roles in the Organization, including the importance of having hearts. In a surprisingly profound statement, Larxene said that having a heart was painful, and wondered if Nobodies like her and Marluxia were better off not regaining their hearts.
As the two walked off together, they started formulating plans to overthrow Organization XIII, setting the mood for Kingdom Hearts: Chain of Memories.

Copy from the Personality Section of KH Wiki
In what may be a connection, written in one of the many Kingdom Hearts novels that correlate with the series, she meets Marluxia for the first time and has just joined the Organization as the sole female. The topic of the Organization's goal is spoken of. Being that she was the newest
recruit and was asking questions, complaining that there was nothing to
do around the castle, and that it was "boring" all the more, Marluxia
repeated to her what Xemnas once told him; which was that they were here
to regain back their hearts. She had gone silent in thought at the
answer, before saying that a heart was not really necessary. She felt
having one was painful, and she was fine with the way things are now,
perhaps implying that she was hurt emotionally for most of her original
self's life, and that lacking a heart keeps the pain at bay.

☁Kingdom Hearts 358/2 Days
Larxene makes a minor appearance in Kingdom Hearts 358/2 Days, only present for a short time in the beginning tutorials. She was disgusted when Roxas awoke on the seventh day and was present when Xion joined the Organization. Larxene trained Roxas in Twilight Town before being sent away to Castle Oblivion. While tutoring Roxas, it was this Nobody's responsibility to teach him how to use magic. Larxene showed a true hatred of having to train Roxas, and seemed to loathe every moment of it. She slipped out the fact there was another Keyblade wielder besides Roxas. Upon being asked who it was, she replied, "Mind your own beeswax." However, if the player speaks to Larxene later in the Grey Area, she seems to begin to acknowledge Roxas's skill, and even considers telling him about her and Marluxia's plot.

☁Kingdom Hearts: Chain of Memories
Larxene is assigned to Castle Oblivion to help conduct experiments on memories; within this castle is Naminé, a young girl and Nobody with the ability to manipulate memories. Sora is led to Castle Oblivion by Marluxia as part of his and Larxene's plan to obtain the power of the Keyblade with which they could take over the Organization. Joining in on this plot is fellow member Axel, one of Larxene's closer friends; however, unbeknown to her or to Marluxia, this is all a ruse on Axel's end, as he is assigned by the Organization as a double agent to gather evidence of their plan and, if their suspicions proved true, eliminate them.
As soon as Sora enters Castle Oblivion, Naminé began manipulating his memories as per Marluxia's orders; soon he begins to gain false memories of Naminé being a childhood friend until all he is unable to remember is her name. At that point, Larxene confronts Sora directly, revealing Naminé is being held hostage in the castle, and attacks him viciously, revealing a lucky charm Naminé had apparently given him years ago, motivating him into remembering her name. In reality, the charm is that of his friend Kairi, having changed shape by Naminé. Larxene fights Sora, taunting him and calling him heartless for "forgetting" about Naminé, before being defeated (something she would never admit) and escaping.
Larxene is later approached by senior member Vexen, who offers to help her, Axel and Marluxia evaluate Sora's power with a replica of Sora's best friend Riku. As per Larxene's suggestion, Vexen decides to have Naminé alter the replica's memory so that it would think it is the real Riku, much to the replica's chagrin. She even goes as far as beating up the replica to subdue it when it tries to resist. As a result, Sora clashes with the replica over protecting Naminé, thus motivating Sora into ascending further up Castle Oblivion.
Finally, Larxene and Marluxia goad Vexen into fighting Sora head on before having him killed by Axel so as to keep Vexen out of their way and to test Axel's loyalties. As soon as Axel is let in on their plot, which seems sure to come to fruition, Axel releases Naminé behind their backs, allowing her to confess to Sora. Their plot having fallen apart, Larxene reveals the nature of Naminé and the Riku Replica to Sora before attacking him in a rage. Larxene is eventually defeated in a brutal battle against Sora, this time fatally, and fades back into darkness

☁The Kingdom Hearts: Chain of Memories manga depicts Larxene's death in an entirely different way. In this version, after she hits Naminé and Donald and Goofy save Sora, Donald casts a Fire spell to melt Sora's Blizzard spell while Goofy spins them around creating a sprinkler effect, getting Larxene wet. Then, when Larxene tries to use her Lightning magic, the water electrifies her instead and incinerates her.
Note: I do not like how her death went in the manga, but I understand they got creative with deaths of the Nobodies due to not wanting to drag the fight on like Shounen Mangas would have.