In many respects Vikohla has diverged from the path her parents set her on, much to their dismay. But she’s still the progeny of a pair of "mad scientists", so she still harbors a love of science, especially the innovative aspects which speak to her creative nature. Her parents, who are predominantly logical thinkers, encourage this side of Vikohla whenever possible and have paid for her Alchemy classes to this end.
Story wise this lab coat originally belonged to Vikohla’s mother and references the size difference between her and her parents. I’m honestly not sure how much use this will get ICly since I would prefer to have her wear the same lab coats as the NPCs studying alchemy in Ul’dah. Perhaps she'll return to the family business someday.