This paper examines the robustness of the optimal lockdown strategy to the postulated social welfare criterion. We show that utilitarianism can, under some conditions, imply a COVID-19 variant of Parfit's (1984) Repugnant Conclusion: for any (interior) lockdown with life periods of low quality, there must be a stricter lockdown that is regarded as better, even though this reduces the quality of life periods even more. On the contrary, the ex post egalitarian criterion (giving priority to the worst-off ex post) implies zero lockdown. Varying between its minimal and its maximal levels, the optimal lockdown is not robust to the postulated ethical criterion. We also identify a general ethical dilemma between the goal of saving lives (modeled by the Survivors Number Count axiom) and the goal of giving priority to the worst-off (Hammond Equity).