My great-grandmother was named
Annie Louella. People talk a lot about variant spellings being a modern idea, but from what I've seen it's really not. It could very well be yet another variant spelling.
Apparently Luila is a town in Bas-Congo in the Democratic Republic of Congo, but I'm guessing that's probably unrelated.
Ancestry.com lists some historical documents for the name Luila, but doesn't offer a meaning or etymology.
Google keeps trying to "correct" to Lulia,
Lula, or
Laila. :/
Sorry if none of that is much help!