Sorry, Dr. Edwards, but when discussing any possible link between Lyme and ME and all the noise associated with both, you opined "...I think we have to assume that some other researchers have looked in to this..."
I cannot say what has been published. But it's common practice in the US at least to take someone who had been diagnosed and treated for Lyme, and who remained symptomatic, but eventually turned sero-negative (or not), and re-brand that individual with ME/CFS.
The thing is, perhaps that old case of Lyme HAS morphed into ME/CFS. Right? Like EBV or an enterovirus, Bb triggered ME/CFS. There is no reason to believe this would be any less a valid occurrence.
Perhaps Lyme lingers but diagnostics fail. The patient tests negative via the CDC's 2T system. It happens. So, Borrelia, in stealth mode, sickens the patient, while clinicians diagnose that individual with ME/CFS, because until SEID has been accepted, it is still primarily a diagnosis of exclusion. Or, maybe, in an ultimate twist, an individual meets the requirements for BOTH diseases - I know at least a few of the members of this forum are a part of that fraternity.
However you approach these possibilities, Borrelia assumes more than just a tad of a correlation, and coincidence does not factor in at all.