If you want to unlock the Phantom Kunai upgrade material, you'll have to defeat Lady Butterfly. More importantly, she further fleshes out the story. Sekiro is a tale of greed, betrayal, and the pursuit of power. Lady Butterfly perfectly compliments that. She goes from a childhood mentor to a traitor who sides with the bandits and most likely wants the power of immortality herself. By not fighting her, you'll not only miss out on an avenue to unlock one of the game's many endings, but you'd also be denying yourself the full scope of the story and gameplay experience.