The Lucas-Washburn equation, describing the motion of a liquid body in a capillary tube, is extended to account for the effect of phase change - evaporation or condensation. The system is found to always possess a stable equilibrium state when the temperature jump across the interface is confined to a certain range. We show that phase change affects the equilibrium height of the meniscus, the transition threshold from monotonic to oscillatory dynamics, and the frequency of oscillations, when present. At higher mass transfer rates and/or large capillary radii, vapor recoil is found to be the dominant factor. Evaporation lowers the equilibrium height, increases the oscillation frequency and lowers the transition threshold to oscillations. For condensation, two regimes are identified: at high mass transfer rates similar trends to those of evaporation are observed, whereas the opposite is found for low mass transfer rates, resulting in an increased equilibrium height, lower oscillation frequencies and a shift of the transition threshold toward monotonic dynamics.