Two unique systems of high-entropy lanthanide oxides (HELO) had been synthesized by the organic-inorganic steric entrapment method to explore the chemical selection rules for solid solution phase evolution under ambient conditions. In contrast to high-entropy alloys, the metallic cations are fitted in the polyhedral sites surrounding by anions. The cation radii vary as a function of oxidation states and coordination numbers. In our HELO systems, we fixed four trivalent cations with similar radii and the fifth cation with larger size. As the radius increases, the octahedral sites become unstable and trigger the existence of a secondary phase. In the second system, a HELO was designed with smaller-sized cations as the variable. A model based on enthalpy, entropy, oxidation energies, and shear modulus was proposed. This result introduces a potential chemical selection guideline for designing structurally stable, high-entropy ceramics.