Just a slight geeky correction of word use... I don't think he meets the guidelines for a psychopath. I get what you're meaning, and think you're probably indicating some anti-social traits. While psychopaths can have that charisma element, and the intelligence, they are generally more unstable. LF isn't unstable, he is able to create really intricate plans and carry them through successfully, even being able to cope with sudden changes to those plans without resorting to extremes. Okay, so he kicked Lysa out the Moon Door, but he would have probably planned to have her killed already. And when he changed his plans to save Sansa, he was able to form up a plan to blame someone else who was also causing him troubles and have them removed.
If he was a psychopath he would likely struggle with that kind of situation. He would also not only have a lack of empathy, but struggle with understanding/interpreting other people's emotions that were not in relation to himself, which would cause him troubles being able to read people so well. I don't think LF is deficient enough to warrant the full label. He's certainly dangerous, and maybe you can argue a lack of empathy, but I would find Gregor Clegane and Hoat more suiting that label than LF.
I would also add, for a complete lack of empathy and more sociopathic traits than LF, Stannis is a really good example.
Yes you are correct. He is not a psychopath in the strict sense of the term. However, I would argue that he does display psychotic tendencies which I do not think are comparable to the Mountain or a man like Vargo Hoat.
According to Wikipedia: "The prototypical psychopath has deficits or deviance in several areas: interpersonal relationships, emotion, and behavior. Psychopaths gain satisfaction through antisocial behavior, and do not experience shame, guilt, or remorse for their actions. Psychopaths lack a sense of guilt or remorse for any harm they may have caused others, instead rationalizing the behavior, blaming someone else, or denying it outright.  Psychopaths also lack empathy towards others in general, resulting in tactlessness, insensitivity, and contemptuousness. Psychopaths can have a superficial charm about them, enabled by a willingness to say anything to anyone without concern for accuracy or truth. Shallow affect also describes the psychopath's tendency for genuine emotion to be short-lived, glib and egocentric, with an overall cold demeanor. Their behavior is impulsive and irresponsible, often failing to keep a job or defaulting on debts."
Yes we can all agree that The Mountain is an extremely violent, sadistic and terrifying man, but what in my opinion makes LF worse is that he is all of these things, yet he manages to hide them behind that "superficial charm". He has this veneer of respectability which conceals a literal madman. He may be able to carefully plan his take overs and take downs and we can never fault him for being able to keep a job or being impulsive, but certainly when we speak of genuine emotion being short-lived and glib and egocentric, this is classic LF.
Also, I think his ownership of the brothel houses speaks not only to good business sense, but also to a certain view of and disconnect from women. They are to be used as Lysa was and then discarded. This is why I fear for Sansa and hopes she finds a way to get out of his hold.