Norway lemming populations cycle, with peak years historically arriving roughly every three to five years, though the regularity has weakened in recent decades. At a peak, density and aggression push young animals to disperse across open country. Dispersal is directional and can involve large numbers moving at once, and lemmings swim, so streams and lakes are attempted rather than avoided. Some drown. That is mortality during migration, not deliberate death.
The cliff footage in the 1958 film White Wilderness was staged. Investigation by the Canadian Broadcasting Corporation in 1983 established that the sequence was filmed in Alberta, far from lemming migration routes, using animals purchased and then driven over a bank into a river.
What is genuinely unsettled is the cause of the cycles themselves. Predation, food quality, winter snow conditions and intrinsic behavioural changes have all been proposed, and recent warming has been linked to the fading of the classic cycle in parts of Fennoscandia.