The way Alyona treated Lizaveta was actually part of the reason Raskolnikov had killed Alyona. .
The narrator from "The Tell-Tale Heart" is obviously not of sound mind. He was constantly trying to convince the reader that he was sane. In fact, that was how he started his story. "True! --nervous --very, very dreadfully nervous I had been and am; but why will you say that I am mad? The disease had sharpened my senses --not destroyed --not dulled them. Above all was the sense of hearing acute. I heard all things in the heaven and in the earth. I heard many things in hell. How, then, am I mad? Hearken! and observe how healthily --how calmly I can tell you the whole story." He is trying to convince the reader that he is not crazy, by constantly stating that he is not mad and then justifying why he is not mad. However, it is clear that he is just trying to convince himself that he is not insane because he is in denial. He also states that he hears all things in heaven and earth, and many things in hell. This suggests that he hears voices and was insane. Another action that proved he was insane was he became obsessed with ridding himself of the old man's eye. He then went on to explain that the old man had never done anything to make the narrator want to kill him, the only reason the narrator wanted to get rid of the old man was his 'pale blue eye, with a film over it.' The eye haunted him, and essentially creeped him out. He believe that the eye was evil, and it should be closed forever. After he killed the old man, the narrator cut him up and dumped the body under the floorboards.
Raskolnikov truly believed he was doing society a favour by killing Alyona. Committing murder is a disturbing thought to begin with, but to justify the crime by believing he was bettering society with her removal is down right creepy and disturbing. There is also the possibility that he might not have felt guilty if he had not killed Lizaveta as well.