<p>Landslide-triggered tsunami can cause extensive environmental destruction and significant loss of life and property. Accurate prediction of their maximum amplitude is crucial for taking effective protective measures. This study employs a two-layer two-phase smoothed particle hydrodynamics (SPH) method for meshless numerical simulations and parameter sensitivity analyses of the Lituya Bay mega-tsunami. Results demonstrate that the two-layer two-phase SPH method effectively and accurately simulates the Lituya Bay mega-tsunami. Based on numerical validation, the subsequent parameter analyses reveal a strong dependence of the maximum landslide-tsunami amplitude on the landslide velocity, irrespective of downstream water depth, with the amplitude increasing substantially as landslide velocity rises. Moreover, landslide density plays a significant role in influencing the landslide-tsunami when the downstream water depth is shallow; however, this influence diminishes in deeper water. Furthermore, the maximum landslide-tsunami amplitude decreases linearly with increasing internal friction angle of the landslide. In addition, this paper develops a nonlinear model that accurately characterizes the relationship between the maximum landslide-tsunami amplitude, the landslide initial velocity, and the downstream water depth. With a coefficient of determination (R²) of 0.9981, the model accurately predicts the maximum landslide-tsunami amplitude, providing valuable theoretical insights and supports for making protection decisions accordingly.</p>