The source for this is an economics paper using old-school macro techniques to measure the correlation between life expectancy and the unemployment rate.
Note that the policy conclusion of the paper includes “It is worth clarifying that with this claim, we do not want to suggest that policymakers should refrain from ordering lockdowns, as necessary lifesaving measures, but rather that, if they decide to do so, they should provide alongside enhanced health and economic support for the most vulnerable portions of the population.”
Moreover, note that the sentence “Unemployment shock is expected to cause 890,000 additional deaths over the next 15 years.” like the whole text you cite seems to suggest a counterfactual of people just continuing their normal work and normal life. While it is surely debatable how effective lockdowns were, their justification was not only saving the lives of old people, but also avoiding an uncontrolled breakdown of the economy; and without a lockdown, many people would probably also have lost their job or stayed home. In some cases, a lockdown ordered by the government may allow more targeted help to those affected.
Note that the policy conclusion of the paper includes “It is worth clarifying that with this claim, we do not want to suggest that policymakers should refrain from ordering lockdowns, as necessary lifesaving measures, but rather that, if they decide to do so, they should provide alongside enhanced health and economic support for the most vulnerable portions of the population.”
Moreover, note that the sentence “Unemployment shock is expected to cause 890,000 additional deaths over the next 15 years.” like the whole text you cite seems to suggest a counterfactual of people just continuing their normal work and normal life. While it is surely debatable how effective lockdowns were, their justification was not only saving the lives of old people, but also avoiding an uncontrolled breakdown of the economy; and without a lockdown, many people would probably also have lost their job or stayed home. In some cases, a lockdown ordered by the government may allow more targeted help to those affected.