Prefer Elizabeth to Margaret by a long shot, but Elizabeth Lilly is a bit too samey in my mind.
Other options:
Elizabeth Rose
Elizabeth Anne
Or, if you like flower names, Margaret Anne, nn Daisy (which is an old-fashioned pet name for Margaret) - personally I love Daisy as a nn. Cute on a little girl, but with a name like Margaret she'd also have the possibility for more professional nn or using her full name when older.
Also with a vowel at the start of the middle name, take care that the initials don't spell out anything eg MAD, MAN, MAP etc