Polycrystalline LuFe0.5Cr0.5O3 perovskite ceramic was synthesized via the solid-state reaction method. Analysis of the electrical modulus reveals a relaxation behavior that does not follow the Debye model. The impedance plots suggest that both grains and grain boundaries contribute to the electric response of the sample. At higher temperatures, an increase in conductivity is observed for both grains and grain boundaries, as demonstrated by Nyquist analysis. The comparable activation energy values of DC conduction and relaxation suggest that similar factors are accountable for both phenomena. Moreover, based on the value of the activation energy of DC conduction, it can be considered that the dominant mechanism for conduction involves thermal stimulation of the electrons from the secondary ionization of oxygen vacancies to the conduction band. Scaling behaviors of electrical modulus, impedance spectra, and electrical conductivity confirm that the relaxation behavior is independent of temperature. Furthermore, the separation of the peak frequencies in electrical modulus and impedance curves confirms the occurrence of migrating carriers at both short and long ranges. It is also evident that there is an increase in carriers with short-range mobility at elevated temperatures. In summary, oxygen vacancies assume a pivotal role in governing both electrical conduction and dielectric relaxation behaviors of the ceramic sample.