Hmm...you're right I don't understand the basis of your complaint. They'll compare patients to healthy controls, and separately, to the asymptomatic Lyme patients. So I don't see how adding the Lyme controls has any bearing on the findings of patients versus healthy controls.
Any time a comparison is made between a group of patients and a control group, it's possible that abnormal results between those groups are due to random chance. Basically, it might just be a meaningless fluke, or "false positive". So p-values are used to set a basic threshold to determine if those results are probably meaningful or not. A typical p-value is 0.05 or 0.01.
When multiple comparisons are made between the patient group and control group, each comparison introduces an additional opportunity for a false positive. So the p-value is "corrected for multiple comparisons", and there has to be a more drastic difference on any of the comparisons for it to satisfy the threshold of probably being meaningful.
So if someone is just comparing blood glutamate levels between patients and controls, it can be pretty easy to show that there is a meaningful difference, even if it's a fairly small difference using a small group of patients and a small group of controls. But if the researcher decides he wants to look at all of the amino acids and adds in another 19, you're going from making 1 comparison to making 20 comparisons. So now there is a big chance that modest differences are due to random chance, and the threshold for showing a statistically significant difference in the levels of any one of the amino acids becomes much much higher.
Similarly, if an extra control group is added, extra comparisons are being made. This might not be a problem if just looking at glutamate levels in ME patients versus healthy controls versus sedentary controls, for example. That's just 2 comparisons: ME glutamate versus one group, then ME glutamate versus the other group.
But if using two control groups to compare ME results for all 20 amino acids, that's 20 comparisons between ME patients and each group, resulting in 40 comparisons being made total. That's a lot of opportunity for false positive results, which makes it much harder to meet the requirements for statistical significance ... the differences now must be pretty dramatic to be considered meaningful. So if only really interested in glutamate, it's probably best to refrain from testing the other 19 amino acids and to seriously reconsider the usefulness of the extra control group.
(This actually happened in
a study which Dr Mark Hallett and Dr Silvina Horovitz co-authored, albeit with a single control group. 22 patients with Focal Hand Dystonia and 22 controls. The study is all about debunking an earlier study showing significant results regarding GABA levels, according to the abstract. But if you read the paper they added in 19 other metabolites which they mostly weren't interested in or even discussing, and dutifully corrected for the excess comparisons. They found a 10% drop in GABA levels in patients, but it needed to be 30% or greater. They would have needed 80 patients and 80 controls for the 10% difference to be statistically significant, according to their own analysis. But the study is still used as a null result, to support the claim that GABA levels are not different in FHD patients versus controls.)
This means that if someone is going to make more than a few comparisons between controls and patients, they need a decent sample size of both patients and controls. If they're making dozens of comparisons, they probably need a pretty big sample size of both patients and controls. And if they're going to then add multiple control groups, the problem pretty much explodes into something completely unmanageable.