A lattice Monte Carlo (MC) model was proposed with the aim of understanding the factors affecting the chiral self-assembly of tripod-shaped molecules in two dimensions. To that end a system of flat symmetric molecules adsorbed on a triangular lattice was simulated by using the canonical ensemble method. Special attention was paid to the influence of size and composition of the building block on the morphology of the adsorbed overlayer. The obtained results demonstrated a spontaneous self-assembly into extended chiral networks with hexagonal cavities, highlighting the ability of the model to reproduce basic structural features of the corresponding experimental systems. The simulated assemblies were analyzed with respect to their structural and energetic properties resulting in quantitative estimates of the unit cell parameters and mean potential energy of the adsorbed layer. The predictive potential of the model was additionally illustrated by comparison of the obtained superstructures with the recent STM images that have been recorded for different organic tripod-shaped molecules adsorbed at the liquid/pyrolytic graphite interface.