Couple of points. There is just not enough info on Lizzie to make any psychological deductions, other than simplistic ones. I have a BA in Psychology, a Master's in Counseling, with an emphasis on Truama and forensic psychology. I am also an RN. I have been in the field of psyc. for 26 years. This isn't to brag, just to give a background that my comments that are psychologically oriented come from education and experience. (that doesn't make me right though)
There is not enough hard facts about Lizzie to make a diagnosis. Much of the talk of her "kleptomania" was exaggerated, I could only find a few possible instances. She didn't seem to exhibit a need for thrills, risks, or excitement, more than the average person. We see no documentation on fire-setting or cruelty to animals either, but again, we just don't know enough. She exhibited little emotion around her parents deaths, but people deal with shock differently. It is curious that she was so obsessed with sending someone upstairs to find Mrs. Borden, that seems to be suspicious. She also talked a lot before the crimes of all the danger the family appeared to be in, but no one else seemed to voice the concern. That seems like an immature attempt to "set the stage" for what was to come. Some witnesses have reported that she genuinely seemed sad while in jail, over the loss of her father, but again, not enough information to know for sure. The thing we are really lacking is video of her. If a profiler/psychologist could hear her voice, see her eye contact, listen to the cadence of her speech, etc. there may be the opportunity of making a better observation, but all we have is words typed on paper. We don't know for sure how she sounded or looked when questioned by police. Obviously in the 1800's there was no video.
Leitskev's comment on the excellent book about psychopaths is on the mark. Many of the people you meet, are friends with, and even love may have "sociopathic/psychopathic" personality traits. these are not mental disorders like depression or anxiety that come-and-go. These are personality traits that form very early in childhood, and are with you until death. A lack of true empathy to others, often masked by "pretending to care" saying the right things so you don't look different. Many politicians, Ambulance workers, Police, CEOs and lawyers have higher than average psychopathic traits. That is why they are successful, a lack of real empathy for others makes them successful in a business where your actions influence others' lives. The vast majority of people like this DON'T go on to commit crimes. But some do, some are good at it. Ted Bundy was charming and lovable, but was sociopathic (the better word than psychopathic) Many people with these traits don't harm others simply b/c they are afraid of getting caught.
Lastly, it is my experience that coincidence is often just coincidence. The human mind is wired to find patterns where none exist. That is why people pay hundreds of dollars for a piece of toast with Jesus face burnt on it. We see patterns in stars, where there is none. I've seen pictures purported to be Mother Mary's face on a wall with paint peeling off. We OVER see, we put too much significance in coincidental things. After JFK assassination, after 911, every little coincidence was given great meaning. I'm not saying there is no connection, just that when I see Morse come the day before the killings, I think perhaps it was not significant. People "snap" after years of slow gradual buildup, I tend to think that if Lizzie killed them, there was no planning, no making an alibi, no forethought other than day by day, month by month dissatisfaction, anger at Abby, worry of not getting the inheritance, anger at father not moving to a better house, frustration building to one day, perhaps hearing a comment that was the "straw that broke the camel's back" she snapped, hacked them up, then backtracked to cover her tracks. Think about school shootings, people going 'postal' etc. The vast majority of the time, people say "he was quiet, shy, but I would have never thought he would do this."