Atmospheric lidars do not penetrate directly most boundary-layer clouds due to their large optical density. However, the lidar's photons are not absorbed but scattered out of the beam. Typically, about half are actually transmitted through the cloud and the other half escape the cloud by reflection in extended diffuse patterns that evolve in time. For all practical purposes, these are the cloud's space-time Green functions (GFs). In a Fourier-Laplace expansion of the space-time GF, the leading term is representative of solar remote-sensing (i.e., steady/uniform source) while higher-order terms correspond to active approaches with temporal- and/or spatial- resolution capabilities. Radiative GF theory is tractable within the limits of photon-diffusion theory and homogeneous clouds. Monte Carlo simulations with realistically variable cloud models are used to extend the range of validity of analytical GF theory with minor modifications. GF theory tells us that physical and optical cloud thicknesses can be retrieved from off-beam cloud lidar returns.