I read a book which said the name was Greek in origin, and it meant, "helper", it was the only time I had seen my name in a name book. I found the book in a university library, so this should be good information.
This looks like a spelling tacky parents would use in place of the rather pretty (though common) Alicia. And it looks like it should be pronounced "ah-LEE-zha", rather than "ah-LEE-sha" or "ah-LEE-see-uh".