Milverton is killed by one of his victims, a woman of quality whose husband died from the shock of the information given to him by the blackmailer. In her grief and anger, she is completely ruthless; she not only empties her handgun into Milverton's chest, she looks down at his dead body and coldly and deliberately grinds the heel of her shoe into his face.
Of course, neither Holmes nor Watson dream that they will witness the murder of Milverton while they are in the process of burgling his home but when this occurs, Holmes' opinions remain unchanged. Moral absolutism would state that murder under any circumstances is wrong, and that the lady responsible should answer for her crime in a court of law. Holmes has a more pragmatic view of it, however. Milverton is a criminal- a blackmailer- and a genuinely evil man. He has ruined countless lives and caused the death of at least one, from shock due to his villainy. It is extremely probable that he caused the deaths of others as well, either through shock or suicide as he casually and cruelly destroyed everything they held dear. Because of the nature of these crimes, Milverton would never have been brought to justice, and Holmes very obviously believes that the lady in question is perfectly justified in taking the law into her own hands. Certainly he will do nothing to aid the police in apprehending her, as his final statement to Lestrade makes clear: “Well, I am afraid I can’t help you, Lestrade,” said Holmes. “The fact is that I knew this fellow Milverton, that I considered him one of the most dangerous men in London, and that I think there are certain crimes which the law cannot touch, and which therefore, to some extent, justify private revenge. No, it’s no use arguing. I have made up my mind. My sympathies are with the criminals rather than with the victim, and I will not handle this case.”