Lily White and Lily Black are the same character. o_o Unless Lily has a twin sister we don't know about.
For your information, Lily Black appears in PoFV, even though lily white/black just are generic enemies in there. But aside from this, Lily Black is generally depicted as some hell of a badass (but still pure) fairy.
Her pure darkness encroaches over everything!Is that so~?The manipulator of the supernatural and the god of war, Hoshiguma Yuugi!Always on the lookout for more strong people!If it's a close-range battle, leave it to her!She wants to announce the coming of spring, and she's gonna do it with danmaku!The fairy herald of spring, Lily White!And Lily Black is here with her!The youkai of darkness, Rumia!