A casual glance at the non-COVID-19 mortality proves that this claim is ludicrous as stated, but it's still worth considering how damaging lockdowns might be to health.
"while there may be multifaceted impacts of intensive government restrictions, including social and economic costs, these are not apparent in short-term increases in mortality. In fact, the World Mortality Dataset appears to show that countries with concerted COVID-19 restrictions have had fewer deaths than in previous years, with the authors estimating that lockdowns may reduce annual mortality by 3–6% from eliminating influenza transmission alone." (https://gh.bmj.com/content/6/8/e006653)
"Data from Peru showing that lockdowns are likely to reduce death risks from common sources such as automobile accidents in the short term, resulting in a reduction in the immediate mortality burden when implemented." (https://gh.bmj.com/content/6/8/e006653)
"The high excess mortality in countries with few restrictions, or less voluntary behaviour change, may not be surprising given the high infectiousness and fatality rate of COVID-19... data from Brazil, the USA and other countries show that moderate containment measures can be insufficient to stop exponential growth of COVID-19 epidemics, in turn leading to an unparalleled mortality burden in the populations affected." (https://gh.bmj.com/content/6/8/e006653)
"There is consistent and robust evidence from many countries that government interventions to control COVID-19 have not been associated with increased deaths from suicide. Indeed, some evidence suggests that the number of deaths from suicide may have dropped in some age groups, particularly children, during the pandemic." (https://gh.bmj.com/content/6/8/e006653)
This is not to suggest that suicides have not risen in some age groups during the pandemic - only that they are not assocated with government interventions. These deaths may (for example) be associated with bereavement due to COVID-19 mortality or anxiety about the risks of COVID-19.
"The association between large outbreaks of COVID-19, government interventions and reduced use of non-COVID health services is well established. However, this association may be due to healthcare services being redirected to handle COVID-19 cases or other impacts of the pandemic itself rather than by lockdowns. In addition, there is evidence that people fear becoming infected by SARS-CoV-2 in healthcare settings and thus stay home rather than attend health services" (https://gh.bmj.com/content/6/8/e006653)
Is the cure really worse than the disease? The health impacts of lockdowns during COVID-19 (2021-07-19)