The lattice cluster theory is used to analyze the pressure dependence of the effective Flory interaction parameter chi(eff) observed in recent small-angle neutron scattering experiments for polymer blends. A description of this pressure dependence in blends requires a theory that contains a minimum of four empirical parameters, three interactions energies and one lattice cell volume, a set smaller than in the seven- or eight-parameter treatments generally-employed with other methods. The conventional liquid mixture philosophy is used for determining this minimal set of parameters as follows : The self-interaction parameters and pure component cell volumes are obtained from fits to pure melt PVT data. A common combining rule then provides the blend cell volume as functions of those for the pure melts, but the common geometric combining rule for the heterocontact interaction energy is found to be grossly inadequate. Hence, this interaction parameter is chosen by fitting to blend data. Explicit comparisons with experimental data for polystyrene (PS) and poly(vinyl methyl ether) (PVME) melts, PS/PVME blends, and PS-b-PMMA (poly(methyl methacrylate)) diblock copolymers demonstrate that this minimal lattice cluster theory provides a good representation of melt equations of state, the composition, temperature, molecular weight, and pressure dependence of the small-angle neutron scattering, the composition dependence of the volume change on mixing, the spinodal curves, and the composition and temperature dependence of the blend correlation length. Additional predictions are presented concerning the stabilization and destabilization of blends by diblock copolymers.