  Dark matter lighter than 10 GeV/c$^2$ encompasses a promising range of
candidates. A conceptual design for a new detector, DarkSide-LowMass, is
presented, based on the DarkSide-50 detector and progress toward DarkSide-20k,
optimized for a low-threshold electron-counting measurement. Sensitivity to
light dark matter is explored for various potential energy thresholds and
background rates. These studies show that DarkSide-LowMass can achieve
sensitivity to light dark matter down to the solar neutrino floor for GeV-scale
masses and significant sensitivity down to 10 MeV/c$^2$ considering the Migdal
effect or interactions with electrons. Requirements for optimizing the
detector's sensitivity are explored, as are potential sensitivity gains from
modeling and mitigating spurious electron backgrounds that may dominate the
signal at the lowest energies.
