Polycrystalline samples of $(R_{0.8}Ca_{0.2})Ba_2Cu_3O_{7-z}$ (R = Lu and Y) were synthesized by a solid-state reaction route, and the phase stabilities were examined by heating at temperatures between $800^{circ}C$ and $900^{circ}C$ in various atmospheres. A comparative analyses of the x-ray diffraction data of the $(Lu_{0.8}Ca_{0.2})Ba_2Cu_3O_{7-z}$ and $(Y_{0.8}Ca_{0.2})Ba_2Cu_3O_{7-z}$ compounds showed that the 123 phase of both compounds is stable under heating in air and $O_2$ of 1 atm. However, contrary to the $(Y_{0.8}Ca_{0.2})Ba_2Cu_3O_{7-z}$ compound, the $(Lu_{0.8}Ca_{0.2})Ba_2Cu_3O_z$ compound was found to become unstable when heated in the low oxygen partial pressure below about 8 % $O_2;in;N_2$, Considering the instability of parent $LuBa_2Cu_3O_z$ compound, this result suggests that the phase stability of Lu-based 123 compounds is sensitive to both the composition and the oxygen partial pressure.