Lattice Monte Carlo simulations of two-dimensional amphiphile solutions are used to examine the accuracy of the mixing properties predicted by lattice theories such as the Flory-Huggins theory, random-solution approximation, and quasichemical approximation. The internal energy, Helmholtz free energy, and entropy of mixing have been calculated from the configurational energy data obtained from the simulations, and the effect of nonrandom mixing on these properties has been determined. The quasichemical approximation predicts the entropy and Helmholtz free energy of mixing accurately for the amphiphile solution, but fails to predict the energy of mixing, due to the presence of microphase (self-aggregation) separation, which is beyond the reach of the quasichemical approximation, a mean-field theory. Helmholtz free energy of mixing is predicted accurately, and the shielding of the solvophobic segments in the microphase leads to small energies of mixing compared to the entropy of mixing.