We numerically investigate the processes responsible for a fog event formed by stratus cloud lowering, observed on December 1-2, 2016, during the experimental campaign in the northeast of France. The observations revealed a complex temporal evolution with stratus followed by a relatively drier period and then its reformation leading to fog formation by stratus lowering. Microphysical observations below a tethered balloon exhibit different vertical profiles of liquid water content and droplet concentration between the stratus and the fog formed below. A simulation at 100-m grid spacing reproduced the main observed characteristics of the cloud life cycle despite a time lag in stratus formation due to large-scale conditions. The advection of cloud water in the stratus and at its top appears crucial to feed the stratus lowering, resulting in radiative cooling, vertical transport, droplet sedimentation, evaporation, and cooling of the sub-cloud layer. The advection of cold or warm air in the lowest 250 m, mainly driven by fine-scale orographic circulations, impacts the fog formation due to stratus cloud lowering. When non-local conditions are favourable, the most important microphysical process to favour fog formation is the droplet sedimentation, leading to the cooling and moistening in the sub-cloud layer by evaporation. Droplet sedimentation appears more efficient when the droplet concentration is low, and a two-moment microphysical scheme more appropriate than a one-moment scheme to reproduce the observed variability of the droplet concentration. Given the predominance of non-local processes on this case study, a three-dimensional high-resolution model appears crucial to perform accurate forecasts of fog by stratus lowering.