This pronunciation would not naturally be the first one an English speaker in the United States would try when they first look at this name. I think only English speakers who are familiar with the way
German is pronounced would naturally think of it as a possibility.
Other common words and names which start with
Lei- (leisure,
Leigh,
Leighton) are pronounced either rhyming with
Lee or Lay by most Americans, so those would be the natural pronunciations of this spelling for most people. In my experience, elderly American women named
Leila usually pronounce their name as LEE-la, though younger generations will often use LAY-la. But you really need to spell it
Lila or
Lyla for most people to try the "lye" pronunciation first.