If you follow the link on this site, it says that
Lila comes from the Indian name
Leela which I assume is pronounced LEE-la.
However, I have known more than one
Lila and have encountered several characters in books (audio) and films named
Lila. Every single one I have encountered pronounced it LYE-la. I assume it is because of the pronunciation of the name
Delilah, especially when Lilah is spelled with the H. Being from
America there is no way that I would look at the name
Lila and think it was pronounced LEE-la. It is
Lila to me, all the way. :o)
Melissa