Vocaloid Megurine Luka has no official personality or fictional biography by her company. It is her vocal description on Crypton that states: voice actress Yu Asakawa provided the 'cool and a little mysterious' vocal. Luka's voice is said to be 'moody yet husky' which makes her suitable for Jazz genre. While Crypton wanted her to sound sexy, the level is softness negated this effect.
The above paragraph is reference to her voice bank traits, not her traits as a fictional character.