You describe a dermatologic condition that causes nearly chalk-white patches on the skin (Vitiligo) in certain areas which on occassion may be associated with streaks of white hair or even white eyelashes (poliosis or leukotrichia). This disorder is felt to be immunologic in origin.
Latisse has not been specifically tested in patients with white eyelashes, as far as I know.
Latisse is an ophthalmic medication that is applied to the base of the eyelashes of the upper eyelid, using a supplied applicator. The effect is to lengthen, thicken and actually darken the eyelashes. The studies reported do not include a group who has vitiligo and/or poliosis and I see no such reports in the literature at this time, so the answer to your question, from a controlled point of view, must be that we do not know!
However, I must admit that your question seems like it would be an excellent study to be considered. Perhaps in some well known university vitiligo clinic, the scientists can design a study, get it through their IRB board, and amass a sufficient number of patients to obtain a scientifically valid answer. I know of no reason why Latisse would be contraindicated in a stable vitiligo patient with poliosis of the eyelashes and in fact there are no listed contraindications in this specific group of patients in the product literature.
Which leads me to the suggestion that you consult your dermatologist and begin a discussion about a course of Latisse treatment with good photographs before and during your therapy for white eyelashes. Then you or your dermatologist can report the results.