From the experts:
This attractive and unique Irish form of Alice can also be found in the phonetic form AILISH. It was introduced into Ireland by the Normans in the French form ALIZ.
Ailis was the name of a notorious fourteenth century witch from Kilkenny. Ailis the Beautiful, a contemporary of King Arthur, had her face covered by a veil so people wouldn't faint (or die) from the sight of her beauty.
Nicknames used in Scotland include Ailie and Lissa.