The steep slopes and shores along lakes and reservoirs in mountainous regions, specifically with glacial history such as the Alps, Alaska or the Himalaya, are prone to terrestrial and subaqueous mass movements. Particularly, increasing temperature due to climate change may affect the stability of mountain slopes because of thawing permafrost and retreating glaciers. Moreover, particular sediment-mechanical properties promote subaqueous mass movements in regions which have experienced glaciation. The occurring mass movements may lead to the generation of a tsunami-like wave when interacting with the water body of a lake or reservoir causing considerable damage to infrastructure and endangering human lives. A prominent example was documented on Lake Lucerne in central Switzerland in 1601. A series of subaqueous landslides following an earthquake led to a tsunami with wave heights of up to 4 m, which flooded parts of the city of Lucerne. Other examples in Switzerland and abroad show that the danger of a lake tsunami is very real. A detailed risk assessment is therefore crucial for mitigation or prevention of such hazard. Current state-of-the-art tools for tsunami modeling are typically used in ocean settings. In this study we evaluate whether models based on hydrostatic and non-hydrostatic non-linear shallow water equations also produce reliable results in lake settings, i.e. for smaller water depth and shorter propagation distance. We perform benchmark tests and compare results to experimental data in order to assess the applicability of hydrostatic versus non-hydrostatic non-linear shallow water equation solvers for tsunami modeling at lake-scale.