During the COVID-19 pandemic, the effects of nationwide lockdowns on health outcomes have been widely studied in Western, developed countries. However, the effects of lockdowns in emerging and developing countries are largely unknown. We used data from India and Bangladesh to study the effect of nationwide restrictions on public movement in Bangladesh in April 2021 on health outcomes, specifically COVID-19 incidence and mortality. India and Bangladesh had nearly identical development of the COVID-19 Delta wave the weeks before the lockdown. We leveraged longitudinal data from the pre-and post-intervention period in both countries in a structural causal model, suggesting that the reported deaths in Bangladesh due to COVID19 would have been similar to 117% higher (95% PI: 72%-170%) in April 2021 had there been fewer restrictions. Further, we used population mobility data from Google to study behavioural changes in the two countries, supporting the hypothesis that the intervention had substantial effects on the mobility trends of the Bangladeshi population, which in turn reduced the number of COVID-19 deaths.