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In this paper, we use a Monte Carlo (MC) simulation based on Geant4 to investigate the influence of four parameters on the spatial resolution of the lens-coupled lutetium yttrium orthosilicate (LYSO) scintillator, including the thickness of the LYSO scintillator, the F-number and minification factor of the lens, and the incident position of the gamma-rays. Simulation results show that when the gamma-rays are incident along the lens axis, the smaller the thickness, the larger the F-number, the larger the minification factor, the higher the spatial resolution, with an isotropic point spread function (PSF). As the incident position of the gamma-rays deviates from the lens axis, the spatial resolution decreases, and the PSF becomes anisotropic. In addition, by analyzing the whole physical process of the lens-coupled LYSO scintillator from gamma-rays to secondary electrons to fluorescence photons, we aim to provide a detailed analysis of the influence of each parameter on the spatial resolution. The results show that the PSF of the secondary electrons energy deposition is almost constant in the simulation, which determines the upper limit of the spatial resolution. Meanwhile, the dispersion process of the fluorescence photons can explain the reason why each parameter affects the spatial resolution.