Or anyone who can help really!
I know this one has mysterious origins, I've read your comments previously, but do you possibly have any more information on it? Just a quick look on google and I've found many variations used on females in the 18th, 19th and 20th centuries: Alefare, Alifare, Alefaire, Alafare and so on. Also Elafare, Ellafare, Ellafair, Elafaire. There's so many.
Was it a surname that became a personal name perhaps? I'd love to know more.