At this point, I'm more inclined to think this was a horrendous, 'heat of the moment' act that occured when the sh*t hit the fan & the truth came out about med school. Lori must have been livid, & the arguement could easily have gotten physical.
From what I've seen & heard, it sounds to me like he really did love her and may have killed her by accident or in desperation when she threatened to tell their families. Of course, this doesn't excuse it, and attempting to cover it up & going mental is reprehensible, but I don't think he's a sociopath like Scott Peterson.
I hardly know enough about the man to speculate as to whether or not he is a sociopath, but there is something seriously and desperately wrong with a person who would lie about graduating from college and lie about being accepted to medical school and actually planning a move across the country based on such a huge lie. How did he think he would get away with such lies?