We modify Larson's lattice model [J. Chem. Phys. 83, 2411 (1985)] and use it to study self-assembly of surfactants in a supercritical solvent by large-scale Monte Carlo simulations. Carbon dioxide and perfluoroalkylpoly(ethylene oxide) serve as prototypes for the solvent and surfactant, respectively. Larson-model type parameters for carbon dioxide and perfluoroalkylpoly(ethylene oxide) are obtained using experimental values of critical parameters and solubility along with a modified Berthelot combining rule. We perform canonical Monte Carlo simulations at a supercritical temperature, varying the number of surfactant head and tail segments, the solvent density and the surfactant concentration. Various properties such as the critical micelle concentration, the aggregate size distribution, and the size and shape of the micelles are evaluated and pseudophase diagrams are constructed. We further investigate the ability of the surfactant solutions to dissolve more solute than solutions without surfactants by calculating the partition coefficient. Water serves as a prototype for the solute and Larson-model type parameters for water are obtained in the same way as for carbon dioxide and perfluoroalkylpoly(ethylene oxide).