We report on successful synthesis and comprehensive study of luminescence spectroscopic properties and decay kinetics of undoped and Ce3+-doped eulytite structure orthophosphate Ba3La(PO4)3 (BLP) upon excitation with UV-VUV and X-ray photons in a wide temperature range. An intrinsic emission located in the UV range is observed for undoped BLP upon both VUV and X-ray excitation. In turn, emission of Ce3+-doped BLP is represented by interconfigurational 5d-4f transitions arising from Ce3+ ions located in two crystallographic sites which demonstrate average decay time of 22 ns and 40 ns upon intracenter excitation. Pulse X-ray excitation results in appearance of slower (μs or longer) decay components and acceleration of the main 5d-4f emission decay component. Host sensitization of Ce3+ emission is well demonstrated by UV-VUV excitation spectra measurements both at liquid helium and at room temperature. Mechanisms influencing the efficiency and time scale of energy transfer from the host to Ce3+ dopant ions are analyzed and discussed while aiming to estimate the potentials of BLP:Ce3+ for scintillator and X-ray phosphor applications.