Reflection, transmission, and absorption of sunlight by clouds plays an important role in climatology. Therefore one goal of lidar remote sensing is the determination of the extinction profile of clouds. We propose a generally applicable retrieval procedure for getting back the extinction profile of a cloud from the lidar return. This method is based on the idea to compare the measured signal with simulated signals which belong to properly parameterized extinction profiles and to search for the minimizing parameter set. The simulation will be done using our variance reduction Monte Carlo program PBS which takes multiple scattering and polarization into account. The search procedure can be deterministic or random search, or a mixture of both. The result of such a retrieval will depend on additional information such as the scattering behavior of the cloud particles which is characterized by their Mueller matrices. Without such additional knowledge the retrieval of the real extinction profile will not be possible, i.e. the inversion is not unique. We shall show some examples. Furthermore, the inversion is ill-posed, i.e., small variations of the lidar return may lead to large variations of the retrieved extinction profile. Our retrieval procedure will allow for a sensitivity analysis of the method and, hence, of this ill-posedness. We shall present such a sensitivity analysis describing the degree of ill-posedness.