Dark matter candidates with masses below 10 GeV/c² hold promise, and a new detector, DarkSide-LowMass, is proposed based on the DarkSide-50 detector and progress towards the DarkSide-20k. DarkSide-LowMass is optimized for low-threshold electron-counting measurements, and sensitivity to light dark matter is explored for various potential energy thresholds and background rates. Our studies show that DarkSide-LowMass can achieve sensitivity to light dark matter down to the level of the solar neutrino fog for GeV-scale masses and significant sensitivity down to 10 MeV/c², taking into account the Migdal effect or interactions with electrons. Requirements for optimizing the detector's sensitivity are explored, as well as potential gains from modeling and mitigating spurious electron backgrounds that may dominate the signal at the lowest energies.