We present a microfounded information mechanism that causes monetary policy transmission lags to be endogenously variable, even when firms are rational and face no exogenous costs of changing prices. Firms must form two distinct expectations, namely, a forecast of future demand and a nowcast of the current unobserved state, because information arrives at different frequencies. We model this setting as a partial-equilibrium, continuous-time optimal stopping problem in which firms receive a continuous noisy signal and a discrete precise signal. Because exercising the timing option to reprice has a sunk opportunity cost, an endogenous inaction region emerges; firms rationally delay adjustment until the discrete signal provides sufficient actionable information. The resulting dynamics reproduce observed Swiss price-adjustment patterns and the highly variable transmission lags of monetary policy. Thus, the framework provides a rational-agent microfoundation for lag heterogeneity.