South Dakota never fully locked down, and the COVID-19 death rate there 4.5 per 100,000. That’s 1/3 the average for the country minus NYC and 1/30th the rate for NYC. And that’s a 5% increase over what the baseline death rate would have been in the state over that time period.
It’s also worth pointing out that nowhere has really “locked down.” Most people are still going to work and leaving the house. Minnesota has found that the stay at home orders reduced contact only by 55%: https://www.minnpost.com/health/2020/05/minnesota-has-update.... Under various scenarios, Minnesota projected a “do nothing” scenario at 57,000 deaths over the course of the pandemic, versus 26,000 deaths if the stay at home order were extended to September. But lifting the order on May 18 results in only a few thousand extra deaths compared to leaving it in place until September.