It was a coincidence each time. The problem is that epidemic waves last a certain amount of time, and politicians tend to enact lockdown after a certain amount of delay because they want to be sure it's really going up and have to wait a few days for the announcements to propagate etc, and then you have to wait a short period before you expect any impact anyway. And then that's when the epidemic naturally goes into decline.

It's trivial to prove this because waves last roughly the same amount of time everywhere, so you can just compare places that went into lockdown with places that didn't and see what happens. The answer is that the waves are the same size and shape regardless of what governments do.

You can also do a regression analysis on "strictness indexes" and case counts, which also yields no correlation. There are such studies:

https://www.frontiersin.org/articles/10.3389/fpubh.2020.6043...

"Stringency of the measures settled to fight pandemia, including lockdown, did not appear to be linked with death rate"

https://thefatemperor.com/wp-content/uploads/2020/11/1.-LANC...

"Rapid border closures, full lockdowns, and wide-spread testing were not associated with COVID-19 mortality per million people"

But you don't need studies. The fact that Sweden didn't lock down and yet has some of the lowest COVID mortality in Europe is decisive. Claims about the effects and necessity of lockdowns were universal and made no exception for Sweden, so the existence of even a single counter-example disproves the theories.