In this perspective, we first review some of the published literature on structural modeling of the mechanical properties of the lung parenchyma. Based on a recent study, we demonstrate why mechanical dysfunction accompanying parenchymal diseases such as pulmonary fibrosis and emphysema can follow a very different course from the progression of the underlying microscopic pathophysiology itself, particularly in the early stages. The key idea is related to the concept of percolation on elastic networks where the bulk modulus of the network suddenly changes when the fibrotic stiff regions or the emphysematous holes become suddenly connected across the network. We also introduce the concept of depercolation as a basis for the rational optimization of tissue repair. Specifically, we use these network models to predict the functional improvements that a hypothetical biological or tissue engineering repair could achieve. We find that rational targeted repair can have significant benefits over generic random repair. This concept may find application in the treatment of lung fibrosis, surgical, bronchoscopic, or biological lung volume reduction, or any future alveolar regeneration or tissue engineering solution to the repair of connective tissue damage of the lung.