We studied the layer-by-layer collapse of molecularly thin films of a model lubricant confined between two atomically smooth substrates. The dynamics of the consecutive expulsion of four molecular layers were found to slow down with decreasing film thickness but showed no evidence for confinement-induced solidification. Using a hydrodynamic model, we show that the sliding friction of liquid layers on top of the solid substrates is approximately 18 times higher than the mutual friction between adjacent liquid layers. The latter was independent of film thickness and in close agreement with the bulk viscosity.