The energies of mixing (interaction parameters) and temperature ranges of stability of solid solutions Lu1 − xLnxVO4 (where Ln is a rare-earth element (REE), scandium, or yttrium) with the zircon structure were calculated using the crystal-energy theory of isomorphous miscibility. It was shown that, with increasing atomic number of REE in the Ce—Lu series, the calculated energies of mixing and critical decomposition temperatures of the solid solutions regularly decrease. The substitution limits at various temperatures, the thermodynamic phase stability, and the temperature of transition to a metastable state were determined. The thermodynamic stability diagram of the REE vanadate solid solutions Lu1 − xLnxVO4 was presented. The results of the work can be used for searching the compositions of matrices and activators of new laser and other materials.