We study theoretically the contribution of thermal fluctuations to the linear theological spectrum of lyotropic smectic A phases at low frequencies. The fluctuations are treated at the Gaussian level; their hydrodynamics is controlled by the undulation/baroclinic mode. In the layer-over-layer sliding geometry, we find an anomalous elasticity varying as /omega/; the corresponding viscous drag is enhanced logarithmically. For other shear geometries we find contributions to the dissipation and elasticity that are in practice small (though formally divergent when the layer spacing is taken to zero). The connection between these results and those given previously for thermotropic smectics, and for block copolymers, is discussed. We outline the possible experimental significance of our findings for the rheology of both aligned and polydomain smectics.