The abstract, discussion, and conclusion do not mention that almost half of the patients (8/20) who did the lightning process (LP) did not participate in this study's survey. It is plausible that those who did not improve would be less likely to want to participate in a followup.
5 of the 12 followed up patients reported that they fully recovered, while 11/12 "reported being back to 85% of normal". These participants had had symptoms for a median of 9.5 months before starting the LP, and were followed up 8.5 months after the LP (which took 3 half days to complete). These results are not surprising considering natural improvement is common within the first few years of long COVID.
In a study which followed 2197 long COVID patients up to two years after symptom onset [1], only 4% of participants had symptoms which did not show signs of improving. ~6.4% of participants fully recovered.
The paper does not include details about what proportion of people did not complete the LP. It also does not say what proportion of those who completed the LP were contacted for followup or what method was used to select those who were followed up.
Considering the small sample size in Arroll et al,
the low followup rate, the unspecified dropout rate for LP, and the potential selection bias of those most likely to improve participating in the LP, it is plausible that the observed improvement and recovery in this study is due to natural improvement.
[1] Servier, C., Porcher, R., Pane, I., Ravaud, P., & Tran, V. T. (2023). Trajectories of the evolution of post-COVID-19 condition, up to two years after symptoms onset. _International journal of infectious diseases : IJID : official publication of the International Society for Infectious Diseases_, _133_, 67–74.
https://doi.org/10.1016/j.ijid.2023.05.007