That areas with some of the highest death rates also had strict lockdowns (Spain, New York) indicates that we are unlikely to find lockdowns had a very large impact on deaths, a view consistent with the recent Lancet paper https://www.thelancet.com/journals/eclinm/article/PIIS2589-5370(20)30208-X/fulltext

It is still too early to say whether a very early lockdown (i.e. before the virus has really taken hold) might help a country achieve a big, long run reduction in deaths but recent events in Australia do not give much cause for optimism.

The impression I get is that some policymakers introduce lockdown measures in a panic, assuming they will produce benefits and paying only lip service to the costs. That is not a good recipe for success.