My middle name is Alesia, which is a variant of Alexis according to my mom. She was inspired by Spanish sounds and pronunciations, so it's pronounced "uh-lay-see-uh".
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".