The hydrological regimes in permafrost-dominated catchments have unique characteristics. However, studies based on plot-scale experiments of runoff generation processes and the factors influencing these processes are limited on the Tibetan Plateau, which is experiencing rapid warming and permafrost degradation. Runoff generation processes were studied on a standard runoff plot (5 × 20 m) in a permafrost-dominated catchment on the Tibetan Plateau with an alpine meadow cover to analyze these processes during the spring–summer transition period (from mid-May to early June) and in the summer months of June and July. The discharge, including surface and subsurface runoff, the soil hydrothermal and moisture conditions, and the meteorological conditions were monitored from May 2018 to May 2019. Partial Least-Squares Path Modeling was used to identify the influencing factors in the two time periods. The lateral subsurface flow at 30–60 cm depth accounted for the majority of the discharge from the runoff plot (>99%) and showed a sharp increase when the soil water contents of the thawed soil layers exceeded a threshold value that varied from 0.41 to 0.52. During the spring–summer transition period, the lateral subsurface flow at 30–60 cm depth was promoted by both event precipitation and the antecedent precipitation with an average runoff ratio of 1.7, indicating that the antecedent moisture condition maintained by the underlying permafrost drives runoff generation via meltwater from snow and frozen soil. In the summer months, the lateral subsurface flow at 30–60 cm depth was directly promoted by event precipitation, especially the moderate precipitation that occurred in this period, with a reduced runoff ratio of 0.5 as a result of deepening of the thawed soil layer from 30 to >60 cm, enhanced evapotranspiration and an increased soil water storage capacity caused by an increase of air temperature and the soil temperature. Prediction models obtained via Multiple Linear Regressions of the identified influencing factors were able to accurately estimate the discharge. This study shows the important role of lateral subsurface flow in runoff generation processes in this permafrost area and the most important influencing factors in different seasons.