Existing stochastic rainfall generators (SRGs) are typically limited to relatively small domains due to spatial stationarity assumptions, hindering their usefulness for flood studies in large basins. This study proposes StormLab, an SRG that simulates precipitation events at 6-hour and 0.03° resolution in the Mississippi River Basin (MRB). The model focuses on winter and spring storms caused by strong water vapor transport from the Gulf of Mexico—the key flood-generating storm type in the basin. The model generates anisotropic spatiotemporal noise fields that replicate local precipitation structures from observed data. The noise is transformed into precipitation through parametric distributions conditioned on large-scale atmospheric fields from a climate model, reflecting both spatial and temporal nonstationarity. StormLab can produce multiple realizations that reflect the uncertainty in fine-scale precipitation arising from a specific large-scale atmospheric environment. Model parameters were fitted for each month from December-May, based on storms identified from 1979-2021 ERA5 reanalysis data and AORC precipitation. Validation showed good consistency in key storm characteristics between StormLab simulations and AORC data. StormLab then generated 1,000 synthetic years of precipitation events based on 10 CESM2 ensemble simulations. Empirical return levels of simulated annual maxima agreed well with AORC data and displayed bounded tail behavior. To our knowledge, this is the first SRG simulating nonstationary, anisotropic high-resolution precipitation over continental-scale river basins, demonstrating the value of conditioning such stochastic models on large-scale atmospheric variables. The simulated events provide a wide range of extreme precipitation scenarios that can be further used for design floods in the MRB.