The computed tomography (CT) chest is a tool for diagnostic tests and the early evaluation of lung infections, pulmonary interstitial damage, and complications caused by common pneumonia and COVID-19. Additionally, computer-aided diagnostic systems and methods based on entropy, fractality, and deep learning have been implemented to analyse lung CT images. This article aims to introduce an Entropy-based Measure of Complexity (EMC). In addition, derived from EMC, a Lung Damage Measure (LDM) is introduced to show a medical application. CT scans of 486 healthy subjects, 263 diagnosed with COVID-19, and 329 with pneumonia were analysed using the LDM. The statistical analysis shows a significant difference in LDM between healthy subjects and those suffering from COVID-19 and common pneumonia. The LDM of common pneumonia was the highest, followed by COVID-19 and healthy subjects. Furthermore, LDM increased as much as clinical classification and CO-RADS scores. Thus, LDM is a measure that could be used to determine or confirm the scored severity. On the other hand, the d-summable information model best fits the information obtained by the covering of the CT; thus, it can be the cornerstone for formulating a fractional LDM.