A lamellar phase is a lyotropic smectic A liquid crystal, composed of parallel bilayers of surfactant separated by water. Coexistence regions between lamellar and isotropic phases form significant parts of the phase diagrams of surfactant solutions. In this work we examine the dynamics of interfaces between a smectic A, and in particular a lamellar phase, and a simple liquid or gas at low Reynolds numbers. Although thermotropic smectic A surface modes are governed by inertia, we have shown that for lamellar phases, modes dominated by surface tension and elasticity play an important role. These modes become possible due to the slip property of lyotropic lamellar phases, allowing relative motion of the surfactant and water layers.