Recently, a number of ternary phase diagrams of lipid mixtures have been constructed using various experimental techniques with a common goal of understanding the nature of lipid domains. An accurate experimental phase diagram can provide rich thermodynamic information and can also be used to extract molecular interactions using computer simulation. In this study, the liquid-ordered and liquid-disordered (lo-ld) phase boundary of DSPC/DOPC/Cholesterol ternary mixtures is simulated in a lattice model using pairwise interactions. The block composition distribution (BCD) technique was used to locate accurately the compositions of coexisting phases and thermodynamics tie-lines in the two-phase region, and the Binder ratio method was used to determine the phase boundary in the critical region. In simulations performed along a thermodynamic tie-line, the BCD method correctly samples the compositions as well as the relative amounts of coexisting phases, which is in excellent agreement with the lever rule. A "best-fit" phase boundary was obtained that has a top boundary closely resembling the experimental boundary. However, the width of the simulated two-phase region is significantly wider than the experimental one. The results show that pairwise interactions alone are not sufficient to describe the complexity of molecular interactions in the ternary lipid mixtures; more complex forms of interactions, possibly multibody interaction or domain interfacial energy, should be included in the simulation.