In lower-income countries, the economic contractions that accompany lockdowns to contain the spread of COVID-19 can increase child mortality, counteracting the mortality reductions achieved by the lockdown. To formalize and quantify this effect, this paper builds a macro-susceptible-infected-recovered model that features heterogeneous agents and a country-group-specific relationship between economic downturns and child mortality, and calibrate it to data for 85 countries across all income levels. The findings show that in low-income countries, a lockdown can potentially lead to 1.76 children's lives lost due to the economic contraction per COVID-19 fatality averted. The ratio stands at 0.59 and 0.06 in lower-middle and upper-middle income countries, respectively. As a result, in some countries lockdowns can actually produce net increases in mortality. In contrast, the optimal lockdown that maximizes the present value of aggregate social welfare is shorter and milder in poorer countries than in rich ones, and never produces a net mortality increase.