The COVID-19 pandemic has profoundly reshaped urban mobility. During the lockdown, workers teleworked if possible and left home only for essential activities. Our study investigates the spatial patterns of essential travel and their socio-economic differences during the COVID-19 lockdown phase in comparison with the same period in 2019. Using data from Columbus, Ohio, we categorized travelers into high, moderate, and low socio-economic status (SES) clusters and modeled travel demand of SES clusters for both phases using spatially weighted interaction models. Then, we characterized the SES variability in essential travel based on frequently visited business activities from each cluster. Results suggest that disparities in travel across SES clusters existed prior to COVID-19 are exacerbated during the pandemic lockdown. The diffused travel pattern of high and moderate SES cluster became localized while the pre-existing localized travel pattern of low SES cluster became diffused. During the lockdown, the low and moderate SES clusters travelled mostly for work with long and medium distance trips, respectively, while the high SES cluster travelled mostly for recreational and other non-work purposes with short distance trips. This study draws some conclusions and implications to help researchers and practitioners plan for resilient and economically vibrant transportation systems in response to future shocks.