Access to COVID-19 vaccines on the global scale has been drastically impacted by structural socio-economic inequities. Here, we develop a data-driven, age-stratified epidemic model to evaluate the effects of COVID-19 vaccine inequities in twenty lower middle and low income countries (LMIC) sampled from all WHO regions. We focus on the first critical months of vaccine distribution and administration, exploring counterfactual scenarios where we assume the same per capita daily vaccination rate reported in selected high income countries. We estimate that, in this high vaccine availability scenario, more than 50% of deaths (min-max range: [56% - 99%]) that occurred in the analyzed countries could have been averted. We further consider a scenario where LMIC had similarly early access to vaccine doses as high income countries; even without increasing the number of doses, we estimate an important fraction of deaths (min-max range: [7% - 73%]) could have been averted. In the absence of equitable allocation, the model suggests that considerable additional non-pharmaceutical interventions would have been required to offset the lack of vaccines (min-max range: [15% - 75%]). Overall, our results quantify the negative impacts of vaccines inequities and call for amplified global efforts to provide better access to vaccine programs in low and lower middle income countries.