Current research indicates that for the identification of lung disorders, comprising pneumonia and COVID-19, structural distortions of bronchi and arteries (BA) should be taken into account. CT scans are an effective modality to detect lung anomalies. However, anomalies in bronchi and arteries can be difficult to detect. Therefore, in this study, alterations of bronchi and arteries are considered in the classification of lung diseases. Four approaches to highlight these are introduced: (a) a Hessian-based approach, (b) a region-growing algorithm, (c) a clustering-based approach, and (d) a color-coding-based approach. Prior to this, the lungs are segmented, employing several image preprocessing algorithms. The utilized COVID-19 Lung CT scan dataset contains three classes named Non-COVID, COVID, and community-acquired pneumonia, having 6983, 7593, and 2618 samples, respectively. To classify the CT scans into three classes, two deep learning architectures, (a) a convolutional neural network (CNN) and (b) a CNN with long short-term memory (LSTM) and an attention mechanism, are considered. Both these models are trained with the four datasets achieved from the four approaches. Results show that the CNN model achieved test accuracies of 88.52%, 87.14%, 92.36%, and 95.84% for the Hessian, the region-growing, the color-coding, and the clustering-based approaches, respectively. The CNN with LSTM and an attention mechanism model results in an increase in overall accuracy for all approaches with an 89.61%, 88.28%, 94.61%, and 97.12% test accuracy for the Hessian, region-growing, color-coding, and clustering-based approaches, respectively. To assess overfitting, the accuracy and loss curves and k-fold cross-validation technique are employed. The Hessian-based and region-growing algorithm-based approaches produced nearly equivalent outcomes. Our proposed method outperforms state-of-the-art studies, indicating that it may be worthwhile to pay more attention to BA features in lung disease classification based on CT images.