It's not surprising that some people with chronic fatigue report benefit from an LP course. That would be expected from most types or faith heading or positive thinking courses. i.e. there are bound to be some anecdotal reports of some people experiencing amazing recoveries, or whatever, after many different types of alternative interventions.
But anecdotal positive reports about the benefit of an untested intervention are no way to assess the value of a potential treatment. That's why we spend millions on clinical trials - it's to try to rule out multiple potential biases. Biases and random events can include such things as: reporting bias, therapeutic allegiance, placebo effect, natural health fluctuations over time, changes of perception re personal abilities, stretching/testing one's self-imposed personal boundaries, and random changes in health.
There are so many reasons why someone with a chronic illness might feel better after attending a positive thinking course, or a faith healing session. But, by any stretch of the imagination, positive thinking, or faith healing, or brain washing, are not treatments for biomedical illnesses such as cancer, HIV, MS, or ME etc. (The reports of cancers reducing in size because of positive thinking have been discredited, to my knowledge. And I always found such reports to be abusive anyway.)
That's not to say that such patients wouldn't benefit from such things, i.e. in terms of increasing the subjective quality of their lives, if such an approach appeals to them - For example, before I had ME, I had a reiki session once, just out of interest - I was interested from a psychological point of view (e.g. a session a calm relaxation and positive vibes - I thought I might benefit from it psychologically, to enhance my subjective sense of well being). And I enjoyed it very much. But it wasn't supposed to be a treatment for anything, and it wasn't sold as a treatment.
However, the major potential danger with LP for ME patients is that it trains patients to believe that they are well, and to ignore their symptoms. And ignoring symptoms can be catastrophic, as we all know too well! It's the opposite of pacing.
Ignoring one's symptoms is not advisable for ME patients because they need to monitor their health in order to avoid post exertional exacerbation.
There are many different reasons why a person might experience fatigue. If someone doesn't experience post exertional exacerbation, then they don't have ME/CFS as defined by the IOM report (which is to be adopted by the CDC.) And I can't comment on how patients without ME/CFS might benefit from LP. I just hope that people understand that it's not a treatment, and is little more than a positive thinking course, and it cannot treat a biomedical illness.