Lensless cameras relax the design constraints of traditional cameras by shifting image formation from analog optics to digital post-processing. While new camera designs and applications can be enabled, lensless imaging is very sensitive to unwanted interference (other sources, noise, etc.). In this work, we address a prevalent noise source that has not been studied for lensless imaging: external illumination e.g. from ambient and direct lighting. Being robust to a variety of lighting conditions would increase the practicality and adoption of lensless imaging. To this end, we propose multiple recovery approaches that account for external illumination by incorporating its estimate into the image recovery process. At the core is a physics-based reconstruction that combines learnable image recovery and denoisers, all of whose parameters are trained using experimentally gathered data. Compared to standard reconstruction methods, our approach yields significant qualitative and quantitative improvements. We open-source our implementations and a 25K dataset of measurements under multiple lighting conditions.