We model the atmospheric response to a chaos-forming event at Juventae Chasma, north of Valles Marineris, Mars, using the Mars Regional Atmospheric Modeling System (MRAMS). Interactions between lake-driven convergence, topography, and the regional wind field steer lake-induced precipitation to the southwest. Mean snowfall reaches a maximum of 0.9 mm/h water equivalent (peak snowfall 1.7 mm/h water equivalent) on the SW rim of the chasm. More than 80% of vapor released by the lake is trapped in or next to the lake as snow. Radiative effects of the thick cloud cover raise mean plateau surface temperature by up to 18 K locally. We find that the area of maximum modeled precipitation corresponds to the mapped Juventae plateau channel networks. At Echus Chasma, modeled precipitation maxima also correspond to mapped plateau channel networks. This is consistent with the earlier suggestion that Valles Marineris plateau layered deposits and interbedded channel networks result from localized precipitation. However, snowpack thermal modeling shows temperatures below freezing for the 12 mbar CO2 atmosphere used in our MRAMS simulations. This is true even for the most favorable orbital conditions, and whether or not the greenhouse effect of the lake storm is included. Moderately higher CO2 pressures, or non-CO2 greenhouse forcing, is very likely required for melting and plateau channel network formation under a faint young Sun. Required warming is ≤ 10 K: global temperatures need not be higher than today. In these localized precipitation scenarios, the rest of the planet remains dry.