The Tibetan Plateau is a key area for research on global environmental changes. During the past 50 years, the climate in the Siling Co lake area has become continuously warmer and wetter, which may have further caused the increase in Siling Co lake area. Based on the Siling Co lake area (2003 to 2013) and climate data acquired from the Xainza and Baingoin meteorological stations (covering 1966 to 2013), we analyzed the delayed responses of lake area changes to climate changes through grey relational analysis. The following results were obtained: (1) The Siling Co lake area exhibited a rapid expansion trend from 2003 to 2013. The lake area increased to 2318 km2, with a growth ratio of 14.6% and an annual growth rate of 26.84 km2·year−1; (2) The rate of air temperature increase was different in the different seasons. The rate in the cold season was about 0.41 °C per ten years and 0.32 °C in hot season. Precipitation evidently increased, with a change rate of 17.70 mm per ten years in the hot season and a slight increase with a change rate of 2.36 mm per ten years in the cold season. Pan evaporation exhibited evidently decreasing trends in both the hot and cold seasons, with rates of −33.35 and −14.84 mm per ten years, respectively; (3) An evident delayed response of lake area change to climate change is observed, with a delay time of approximately one to two years.