I live in the US and I've only ever heard
Leila pronounced like lay-la.
My preference for ly-la is
Lilah. It looks the most versatile and easier to mature into.
I think
Lyla leans more young and trendy, but
Lilah could fit any age.
I agree
Lila would be annoying with the lee-la/ly-la problem.
Another option might be
Laila-- that one could grow on me, but I still prefer
Lilah at the moment. (plus even though
Laila looks more like ly-la than
Leila does, it can also be pronounced lay-la).