Electrical-resistivity and magnetic-susceptibility measurements under hydrostatic pressure up to p = 2.75 GPa have been performed on superconducting LiFeP. A broad superconducting (SC) region exists in the temperature - pressure (T-p) phase diagram. No indications for a spin-density-wave transition have been found, but an enhanced resistivity coefficient at low pressures hints at the presence of magnetic fluctuations. Our results show that the superconducting state in LiFeP is more robust than in the isostructural and isoelectronic LiFeAs. We suggest that this finding is related to the nearly regular [FeP_4] tetrahedron in LiFeP.