A couple of thoughts 
@Marky
1). If the "control" also go on to have LP later this makes long term follow up meaningless. 
Given ME is a fluctuating condition and patients can have relapses that last months, plus some are lucky enough to go through less severe patches (though still ill), to get a true picture of whether any effect is down to LP or not there should be several follow up points - I would suggest maybe 3 or 6 months, then a year, then maybe 18 months.
2).  LP is a proprietary therapy and participants are have to agree not to discuss the therapy with others.  This being the case there is no reason why there couldn't be a control arm, given a treatment similar to LP but with vital differences,  as being honest about symptoms.
Again several follow up points should be included.