Superconducting nanowire single photon detectors (SNSPDs) are a key enabling technology for optical quantum information science. In this paper we demonstrate a SNSPD fabricated on lithium niobate, an important material for high speed integrated photonic circuits. We report a system detection efficiency of 0.15% at a 1 kHz dark count rate with a maximum of similar to 1% close to the critical current at 1550 nm wavelength for a parallel wire SNSPD with front side illumination. There is clear scope for improving on this performance with further materials optimization. Detector integration with a lithium niobate optical waveguide is simulated, demonstrating the potential for high single photon detection efficiency in an integrated quantum optic circuit.