Her character model is a palette swap of summoner, Belgemine. Ginnem also has white makeup on her face.
Lady Ginnem was a summoner who lost her life while attempting to acquire the aeon Yojimbo in the Cavern of the Stolen Fayth two years before Yuna's pilgrimage. Lulu was her sole guardian and never truly got over her grief of failing in her duties.
If the party revisits the Farplane in Guadosalam after Tidus mentions Seymour's departure for Macalania Temple, Lulu attempts to speak with Lady Ginnem, but she doesn't respond. When Tidus asks who she's trying to speak with, she says it's none of his business. Though, she does apologize to him since it's not his fault and she wonders why Lady Ginnem isn't in the Farplane (Lulu didn't realize that Lady Ginnem was never sent).
When Yuna and the party stop to inspect the Cavern during her pilgrimage, Lulu is hesitant to enter as it brings back bad memories. Upon reaching the fayth, Lady Ginnem appears in an unsent form. Lulu attempts to apologize for her failure, but Ginnem is no longer human and summons Yojimbo to fight the party. Lulu faces her demons and lays the spirit of her former charge to rest on the Farplane. After the battle, Yuna gets Yojimbo as an aeon.
Lulu can pay Lady Ginnem a visit on the Farplane after her spirit was sent there.
Lady Ginnem is not fought directly, rather via aeon, Yojimbo.