No, Lapis didn't pick her because she's blue.
Faceclaim: Sicily von Claude from Kenja no Mago
A longtime resident of Mitakihara, Kurumi Igarashi was, for much of her life, pretty ordinary. For... a given definition of ordinary. Born to a middle-class family of martial artists, she was taught an ensemble of different styles from childhood, and would eventually wind up establishing her own dojo towards Mitakihara's outskirts- the Igarashi School of Anything-Goes Martial Arts.
Said dojo wound up making it out of a certain "cataclysmic superstorm" mostly unscathed, and so became a major pillar of the local community during rebuilding efforts, mostly by accident. During this time, in spite of the difficulties of rebuilding, Kurumi married her childhood sweetheart- one Saki Mineha.
It wasn't meant to last, unfortunately; four years on, Saki would pass away from a terminal illness, leaving Kurumi to grieve mostly alone, with only a handful of students around to give her purpose.
Four years later, she ran into the Incubator who had yet to name himself 'Lapis'- still somewhat reeling from the psychic attack that had changed him, and looking for someone to test his new magi template with. Kurumi was initially skeptical- one of her students had been approached by Kyuubey not too long prior, and fortunately was intercepted by a bow-wielding woman with pink hair that Kurumi didn't know yet, so she already to an extent knew what the Incubators' deal was. It took... convincing.
Ultimately, of course, she would agree to a contract with Lapis, and so became the first of his magi- a magical girl who would never become a Witch.
The powers granted to her by this contract come in two main forms, plus a secret third. Her monocle, and her watch. Specifically chosen by Lapis, Kurumi has the ability to gaze across time and space using her monocle, and the ability to cross time using her watch. These both have significant limitations; the monocle can only observe one time period at a time, and requires active focus to adjust, making it less useful the less time she has to use it. The watch, meanwhile, requires significant coordination to use effectively, as demonstrated by Kurumi's accidental crossing into the wrong timeline seen previously. It can technically move forwards and backwards through time, but both Kurumi and Lapis have agreed that using it this way is a bad idea.
Kurumi's monocle mostly gets used for gathering information from across timelines; it can technically be used in combat, but doing anything more involved than seeing more than a second or two into the future tends to be too much to handle in an active fight. It's very useful for ambushes, though.
Kurumi does also have a dose of lightning in her powerset, however it's not particularly strong by itself; mostly she uses it in combination with her own physical strikes.