There are some cases where I prefer the NN to the full name. (Lily, Lucy, etc.) Most people seem to think NNs are always shorter than full names, so it might be more practical to name someone Anniken and have the NN be Anna. Just my two cents. ;)
Um...Lily and Lucyare full names; they're not nicknames for anything unless you want them to be (and are pretentious, imho). Lucy is just the English form of Lucia, and Lily is simply a transference of the flower's name.