I've run into this with the name
Alisha,
Elisha or
Alicia a lot in my life, because I grew up with many of those. For
Felicia, I would say fuh-LEE-sha, just like I would say ah-LEE-sha for Alicia/Alisha, but there were a good number of people who would correct me and say "it's LISH-a". I think it was maybe influenced by the large number of Trishas and Tricias that were around at the same time - they of course were always TRISH-uh, never TREE-sha or anything like that.