Basic Profile: Lulu is a woman who is very skilled in the art of magic use - especially Black Magic. Using the power of these devestating spells, Lulu is able to easily take advantage of a target's elemental weakness to cause massive amounts of damage to almost any fiend.
Battle expirence aside, Lulu is a woman who had lived on the Isle of Besaid for most of her life. She grew up with Yuna, Wakka, and Chappu, Wakka's younger brother who was killed by Sin several years prior.
Lulu is looked up to by Yuna. She offers emotional support to the young summoner, helping to guide her through her pilgrimage. Though she does seem serious and stern a good deal of the time, deep down this woman has a warm heart and only wishes for the best for those that surround her.
In-depth Biography: Please note: This information is spoiling. Don't read on if you don't want to be spoiled!
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As stated, Lulu grew up in Besaid. Her relationship with Wakka's brother, Chappu, was quite the serious one. She was romantically involved with him and the two were to wed, but of course, the tragedy struck and he was killed, ruining Lulu's dreams of spending her life with the man. She never really did get over it, as seen throughout the course of the game, but slowly, the wounds do begin to heal, though not completely.
As a young woman, Lulu accompanied two Summoners on their pilgrimages. None of the summoners ever made it to greet Lady Yunalesca and summon the Final Aeon. The first one was Lady Ginnem. This summoner did not make it very far as her last stop was the Cavern of the Stolen Fayth in the Calm Lands. Lulu was unable to protect the summoner from death and Lulu kind of saw this as failing as a guardian. Many years later, during FFX, there is an optional sidequest to obtain the Aeon Yojimbo in the cave - there the party can battle with Lady Ginnem and her Aeon. Lulu decided to do so as she sees herself as 'owing' it to send her spirit to the farplane.
The second one she had went with was Father Zuke - A male summoner that ended his pilgrimage in the Calm Lands.
Of course, many years later Lulu became Yuna's guardian, but she objected to it as she knew quite well how serious the summoner's job was, but no matter what she said to Yuna, she was unable to stop her, so instead, she decided to venture with the young woman who was like a sister to her and protect her on her journey.