Psychopathic SKs can come in many forms. From narcissistic ones (the Alcala type) to the sexual predator type (for example Ridgway) to the mission driven type (for example Glaze), just to name some. But to make it not too easy, for example mission-driven killers can come as delusional type, as psychopathic or even a sociopathic type as well. The delusional mission-driven type is like Mullin for example or in it's extremer form like Chase, the Vampire of Sacramento if you have heard of him. However, LISK, while showing some aspects of mission-driven behavior is too high organized for a delusional type.
The mission-driven psychopathic type can pop up as self-justifying type, like Billy Glaze, for basically formed in his mind an opinion, that all native American women should be raped and killed for ethnic reasons and therefore justified what he did with that mission. The extreme form is Mohammed Atta, I call him "the terrorist, who never got laid". Kind of a Black Paladin syndrome. His whole life was built on the extreme religious model, his father had imprinted on him and thus, he was never successful with women. So at some point, he corrected that picture and told everyone "bah women, I have no time for it, I'm a holy warrior". And at some point, that led him right into the WTC.
And we have the sociopathic version of the same picture. Colder, more controlled, without the direct rage, that fuels the psychopath. He is even more manipulative but less prone to direct action. He pushes others forward to execute that action, he dreams of. The fantasies of mission-driven sociopaths are big and they circle around power as ultimate safety measure. The logical end is normally disaster, because the "safety measure" is not achievable without killing everybody who is perceived as "different". Osama bin Laden, the small boy who learned helplessness when bullied as kid in school and learned to use religion as weapon, that's a good example. Or Adolf Hitler, the gas-victim from WWI and painter without success.
And to make the point clear, I talked here only about the mission-driven types. There are so many more. The problem can't even be described by just a single handy label, much more it can't be solved that way.
With LISK we talk, IMO, either about the psychopathic version or the sociopathic whose dream lack from followers. In the first case, he will appear in daily life rather meek, avoiding to pull too much attention. In the second version (which I suspect), he will be good at what he does in his daily job, but he will appear more effective than arrogant. He will be able to organize things, for example small work parties and he will be in situations, he has to lead people, clear in his instructions and a straight forward leader. He would be in both cases highly manipulative and take care, that people like him.