We have studied the temperature-composition phase diagram for a dilute surfactant model solution on the square lattice through Monte Carlo simulations. A micellar region and a solubility line were identified from the measurement of different properties, among which the volume fraction of aggregate, specific heat, and convergence of relaxation from different initial conditions. We have compared properties of the above system with those of a symmetric lattice solution in the dilute regime. Comparison of data allow an interpretation of the micellar phase as a transition region between a microscopically homogeneous phase and a solid phase.