A novel high-performance computing algorithm, developed in response to the next generation of computational challenges associated with burning plasma regimes in ITER-scale tokamak devices, has been tested and is described herein. The Lorentz-orbit code for use in stellarators and tokamaks (LOCUST) is designed for computationally scalable modelling of fast-ion dynamics, in the presence of detailed first wall geometries and fine 3D magnetic field structures. It achieves this through multiple levels of single instruction, multiple thread parallelism and by leveraging general-purpose graphics processing units. This enables LOCUST to rapidly track the full-orbit trajectories of kinetic Monte Carlo markers to deliver high-resolution fast-ion distribution functions and plasma-facing component power loads. LOCUST has been tested against the prominent NUBEAM and ASCOT fast-ion codes. All codes were compared for collisional plasmas in both high and low-aspect ratio toroidal geometries, with full-orbit and guiding-centre tracking. LOCUST produces statistically consistent results in line with acceptable theoretical and Monte Carlo uncertainties. Synthetic fast-ion D-α diagnostics produced by LOCUST are also compared to experiment using FIDASIM and show good agreement.