Molecular sorting is a fundamental process responsible for the organization of matter in eukaryotic cells. It allows cells to counteract the homogenizing effect of diffusion, and to maintain different functional properties in appropriated membrane subregions. A recent phenomenological theory proposes that this process could emerge from two main physical phenomena, (a) phase separation induced by molecular self-aggregation and (b) vesicle nucleation due to a coupling between particle presence and membrane spontaneous curvature. To further explore this theory preceding works introduced a minimal lattice gas model, in which the membrane is described as a flat two dimensional surface, and investigated its stationary state numerically.