Pathological lung segmentation (PLS) is an important, yet challenging, medical image application due to the wide variability of pathological lung appearance and shape. Because PLS is often a pre-requisite for other imaging analytics, methodological simplicity and generality are key factors in usability. Along those lines, we present a bottom-up deep-learning based approach that is expressive enough to handle variations in appearance, while remaining unaffected by any variations in shape. We incorporate the deeply supervised learning framework, but enhance it with a simple, yet effective, progressive multi-path scheme, which more reliably merges outputs from different network stages. The result is a deep model able to produce finer detailed masks, which we call progressive holistically-nested networks (P-HNNs). Using extensive cross-validation, our method is tested on multi-institutional datasets comprising 929 CT scans (848 publicly available), of pathological lungs, reporting mean dice scores of 0.985 and demonstrating significant qualitative and quantitative improvements over state-of-the art approaches.