Systematic effects arising from cosmic rays have been shown to be a significant threat to space telescopes using high-sensitivity bolometers. The LiteBIRD space mission aims to measure the polarised Cosmic Microwave Background with unprecedented sensitivity, but its positioning in space will also render it susceptible to cosmic ray effects. We present an end-to-end simulator for evaluating the expected scale of cosmic ray effects on the LiteBIRD space mission, which we demonstrate on a subset of detectors on the 166 GHz band of the Low Frequency Telescope. The simulator couples the expected proton flux at L2 with a model of the thermal response of the LFT focal plane and the electrothermal response of its superconducting detectors, producing time-ordered data which is projected into simulated sky maps and subsequent angular power spectra.