Doujins vary on her relationship to her canonical counterpart - some depict her as an alternate persona, and others as an entirely different character - but nevertheless she is frequently depicted as a more serious counterpart to the cheerful Lily White.
ZUN eventually confirmed that Lily Black is just Lily White dressing like Shiki Eiki. Given all the other fairies in the stage do the same, it's possible that the outfit is a uniform of sorts.
