Lien 2019: some analysis and thoughts
The day 2 differences for patients in lactic production, and power at the gas exchange threshold (GET), look pretty interesting – though the differences aren't huge. However, the big differences
between patients and controls seen on for almost every outcome at CPET1 and CPET2 are harder to interpret, because it looks like the controls are poorly matched (they are probably not really sedentary). The study made a large number of comparisons and did not correct for this statistically, though the most interesting findings would survive correction. It is a small study and the findings need replication, of course.
Poorly matched controls?
Controls' VO2 peak results were dramatically higher than patients' (37 versus 24 ML/KG/min), a much bigger difference than I remember seeing in previous studies. Conntrols "exercise less than twice a week on a regular basis ", but the results indicate they were quite fit (see Fig 2b in a new large European study of female healthy non-smokers with a similar BMI). This study took place in Norway and I believe that studies have shown that Norwegians are fitter than Americans who make up participants in most studies to date. So these controls may not be particularly sedentary.
Also, controls have a significantly low BMI than patients (22.0 versus 25.2) and are younger (age 34 versus 37) and both these factors (esp BMI) would lead to a higher VO2 peak.
The authors say that lower levels of blood lactate in trained athletes is due to faster lactate clearance, rather than fast at lactate production. And it is possible that greater fitness and (possible) faster lactate clearance explains the why controls comfortably outperformed patients in most measures in this study. Previous (single CPET) studies have inconsistent results on lactate vs conntrols, as the paper notes, so this is one more study adding to the uncertainty. The new study uses CCC criteria vs Fukuda in older lactate studies, but typically 90% of Fukuda patients have PEM so that might not be a significant factor.
Day one versus day 2
But poorly matched controls would not explain the findings of differences between day one and day two, and I think these are the meaningful findings from this study.
Patients producing significantly more lactate per watt output might be down to controls being much fitter and poorly matched. More interesting is that there is a small but significant decrease in lactate for controls on day two compared with a similarly small increase in patients. These changes, and the difference between patients and controls has a P value of <0.001 and so would survive statistical correction for the 50+ comparisons made in the study.

The authors say that regular endurance training improves lactate clearance and they propose that the day one exercise test leads (rapidly!) to fast at lactate parents and so lower lactate levels on day two. This is Interesting, though it is a pity there isn't other data to support this, such as lactate levels in controls in other 2-day maximal exercise tests.
Other lactate results also show high lactate levels in patients, but not controls, on day two. There is also higher lactate at gas exchange threshold (p = 0.03, which would not survive correction).
Higher lactate is also seen at the at the lactate turn point, LT, (effectively the switch to more anaerobic respiration, and usually seen as the underlying process measured by gas exchange threshold). The difference is also seen in power at onset of blood lactate accumulation, OBLA, which is the power output at 4 nmol per litre of lactate.

Replication of reduced power at GET on day-2

P = 0.02 would certainly not survive statistical correction in this study, but it seems fair to include it as it is really a comparison with other studies on a single measure.
No difference in delta peak VO2
Another study fails to find a drop in day to VO2 peak for patients. I agree with
@Snow Leopard that non-athletes are unlikely to exercise to total exhaustion. But the initial finding from Workwell were held to be important because healthy controls and patients with cardiopulmonary diseases did not show a drop in VO2 peak on day two. I am not sure there is an obvious reason to assume a difference in motivation between mecfs patients, other patients and sedentary controls.

Fig 2B CPET1 vs 2
differences for mecfs and controls
Note that there is actually a lot of variability in controls (suggesting that replication isn't always so reliable on day two) and a serious overlap with patients data. (I don't remember other studies showing so many individual data points, which is particularly helpful, especially in these rather small studies.)
The paper said that participants were given "strong vocal encouragement during the test". Heart rate and the RER both indicate high and similar level of effort in patients and controls in the study at VO2 peak. The authors also said that a 10% drop from day one was needed to be considered significant, and it doesn't look like we're even getting close to that.
What does it all mean?
I have to say, I am surprised we don't see a much bigger difference on day two between patients and controls in the studies. PEM is such a dramatic symptom and exercises such a big issue for us.
And why do lactate levels increase on day two in patients when they decrease in controls? What is the significance of reduced power at the gas exchange threshold, but not at VO2 peak?
Beats me.
However, I think this is important:
the longer effect on the delayed PEM is «lost». You will have PEM day 2, but very often to a greater extent day 3, 4 and 5.
There is a lot of variation between patients in how long it takes for full PEM to cut in. But the point is very important. Given that these type of studies aim to probe what's happening with PEM, it is surprising that they don't routinely measure PEM in patients before the day 2 test. Perhaps having good PEM data would help to unpick the slightly confusing results from these two days maximal exercise studies.