I have an explanation for the LKJ Ive seen over the past 30 years - from a number of teachers and sources, including some who's youtube clips have been presented here as evidence for. I'd just like to add this is all from direct first hand experience - from my own teachers at the time, to attending workshops, to having guys come into our class to demonstrate their "powers"
My explanation is that it relies totally on a steady process of grooming students using a variety of techniques (most often making them feel "special" in some way) linked in with a teacher assuming an important role in the student's life. The intensity of that ranges from paying lots of money for everything Sifu organises through to outright cult- like worship.
At no time has any LKJ, from numerous sources, ever worked on myself or any of students or colleagues present. In fact in some cases, again with people often put forward as "masters of the art", it has failed spectacularly.
I have had very interesting experiences with some teachers, such as Vincent Chu - who incidentally voiced the opinion that while subtle "energy" work can be useful between teacher and student, the thought that it can be used in any kind of self defence situation or to affect people who have not been subject to the "process" is misguided at best.
I do not discount the effects of psychological work, hypnosis, flinch work, subtle physical and psychological "body mechanics" and similar. However the notion of LKJ as it is most usually put forward has in my experience been discredited. In short I do not believe that a person can emit some force from their body that physically effects another in such a major way as making them fall, stop their movement, etc. However I always like to maintain an open mind and have a standing invitation open to anyone who is willing to demonstrate such powers