Icy, Icey, and Icie have turned up as given names in the Southern USA for years. They are probably originally pet forms of names such as
Bernice and the like, which were sometimes pronounced with the final syllable like the word "ice" in the 19th century.
Tiny and Fate are probably uses of the words. Since it's a girl's name, Lemon could be considered a plant name like
Rose or
Magnolia, but it might also be a surname transfer.
Mace is a medieval pet form of
Matthew, IIRC. I am presently visiting my relatives in Tennessee and so don't have my reference books to check. :)