Global storm-resolving models (GSRMs) are the upcoming global climate models. One of them is a 5-km Icosahedral Nonhydrostatic Weather and Climate Model (ICON). Its high resolution means that parameterizations of convection and clouds, including subgrid-scale clouds, are omitted, relying on explicit simulation but still utilizing microphysics and turbulence parameterizations. Standard-resolution (10-100 km) models, which use convection and cloud parameterizations, have substantial cloud biases over the Southern Ocean (SO), adversely affecting radiation and sea surface temperature. The SO is dominated by low clouds, which cannot be observed accurately from space due to overlapping clouds, attenuation, and ground clutter. We evaluated SO clouds in ICON and the ERA5 and MERRA-2 reanalyses using about 2400 days of lidar observations and 2300 radiosonde profiles from 31 voyages and Macquarie Island station during 2010-2021, compared with the models using a ground-based lidar simulator. We found that ICON and the reanalyses underestimate the total cloud fraction by about 10 and 20%, respectively. ICON and ERA5 overestimate the cloud occurrence peak at about 500 m, potentially explained by their lifting condensation levels being too high. The reanalyses strongly underestimate fog or near-surface clouds, and MERRA-2 underestimates cloud occurrence at almost all heights. Outgoing shortwave radiation is overestimated in the reanalyses, implying a ”too few, too bright” cloud problem. Thermodynamic conditions are relatively well represented, but ICON is less stable than observations and MERRA-2 is too humid. SO cloud biases are a substantial issue in the GSRM, but it matches the observations better than the lower-resolution reanalyses.