Carbon dioxide is an essential atmospheric component in martian climate models that attempt to reconcile a faint young sun with planetwide evidence of liquid water in the Noachian and Early Hesperian. In this study, we use mineral and contextual sedimentary environmental data measured by the Mars Science Laboratory (MSL) Rover Curiosity to estimate the atmospheric partial pressure of CO2 (PCO2) coinciding with a long-lived lake system in Gale Crater at similar to 3.5 Ga. A reaction-transport model that simulates mineralogy observed within the Sheepbed member at Yellowknife Bay (YKB), by coupling mineral equilibria with carbonate precipitation kinetics and rates of sedimentation, indicates atmospheric PCO2 levels in the 10s mbar range. At such low PCO2 levels, existing climate models are unable to warm Hesperian Mars anywhere near the freezing point of water, and other gases are required to raise atmospheric pressure to prevent lake waters from being lost to the atmosphere. Thus, either lacustrine features of Gale formed in a cold environment by a mechanism yet to be determined, or the climatemodels still lack an essential component that would serve to elevate surface temperatures, at least locally, on Hesperian Mars. Our results also impose restrictions on the potential role of atmospheric CO2 in inferred warmer conditions and valley network formation of the late Noachian.