In a relatively recent paper by the authors, an explicit (i.e. non iterative) formula was provided for recovering the overlap factor in an aerosol lidar equipped with a N2/O2 Raman channel close to an elastic one to retrieve the aerosol extinction coefficient. One of the advantages of that formula is that it allows for the estimation of the impact of an erroneous lidar ratio in the retrieved overlap function. In the cited paper, the equation that relates the retrieved overlap function to the true one and the error on the assumed lidar ratio was given with almost no proof, on the grounds that its derivation was “boring and cumbersome, but otherwise straightforward”. After having discussed that equation with some interested researchers, it turns out that its derivation is not perhaps that straightforward. Therefore, we provide here its derivation. As a subproduct of that derivation, we propose a streamlined, two-step explicit formulation to retrieve the overlap function.