Cathepsin C (CatC) is a cysteine dipeptidyl aminopeptidase that activates most of tissue-degrading elastase-related serine proteases. Thus, CatC appears as a potential therapeutic target to impair protease-driven tissue degradation in chronic inflammatory and autoimmune diseases. A depletion of proinflammatory elastase-related proteases in neutrophils is observed in patients with CatC deficiency (Papillon–Lefèvre syndrome). To address and counterbalance unwanted effects of elastase-related proteases, chemical inhibitors of CatC are being evaluated in preclinical and clinical trials. Neutrophils may contribute to the diffuse alveolar inflammation seen in acute respiratory distress syndrome (ARDS) which is currently a growing challenge for intensive care units due to the outbreak of the COVID-19 pandemic. Elimination of elastase-related neutrophil proteases may reduce the progression of lung injury in these patients. Pharmacological CatC inhibition could be a potential therapeutic strategy to prevent the irreversible pulmonary failure threatening the life of COVID-19 patients.