What exactly do those studies compare? How countries without lockdown coped in the same wave?

Lockdowns were called because hospitals were at capacity and immediate risk of failing to keep up service - as is currently again the case e.g in Germany.

Remember, the first lockdowns in Europe were mandated after hospitals in Italy were forced to conduct triage. (The "who do I have to let die" kind of triage)

Why did that not happen in whatever control groups the studies were looking at?