Auxiliary diagnosis of different types of cystic lung diseases (CLDs) is important in the clinic and is instrumental in facilitating early and specific treatments. Current clinical methods heavily depend on accumulated experience, restricting their applicability in regions with less developed medical resources. Thus, how to realize the computer-aided diagnosis of CLDs is of great clinical value. This work proposed a deep learning-based method for automatically segmenting the lung parenchyma in computed tomography (CT) slice images and accurately diagnosing the CLDs using CT scans. A two-stage deep learning method was proposed for the automatic classification of normal cases and five different CLDs using CT scans. Lung parenchyma segmentation is the foundation of CT image analysis and auxiliary diagnosis. To meet the requirements of different sizes of the lung parenchyma, an adaptive region-growing and improved U-Net model was employed for mask acquisition and automatic segmentation. The former was achieved by a self-designed adaptive seed point selection method based on similarity measurement, and the latter introduced multiscale input and multichannel output into the original U-Net model and effectively achieved the lightweight design by adjusting the structure and parameters. After that, the middle 30 consecutive CT slice images of each sample were segmented to obtain lung parenchyma, which was employed for training and testing the proposed multichannel parallel input recursive MLP-Mixer network (MPIRMNet) model, achieving the computer-aided diagnosis of CLDs. A total of 4718 and 16290 CT slice images collected from 543 patients were employed to validate the proposed segmentation and classification methods, respectively. Experimental results showed that the improved U-Net model can accurately segment the lung parenchyma in CT slice images, with the Dice, precision, volumetric overlap error, and relative volume difference of 0.96±0.01, 0.93±0.04, 0.05±0.02, and 0.05±0.03, respectively. Meanwhile, the proposed MPIRMNet model achieved appreciable classification effect for normal cases and different CLDs, with the accuracy, sensitivity, specificity, and F1 score of 0.8823±0.0324, 0.8897±0.0325, 0.9746±0.0078, and 0.8831±0.0334, respectively. Compared with classical machine learning and convolutional neural networks-based methods for this task, the proposed classification method had a preferable performance, with a significant improvement of accuracy of 10.74%. The work introduced a two-stage deep learning method, which can achieve the segmentation of lung parenchyma and the classification of CLDs. Compared to previous diagnostic tasks targeting single CLD, this work can achieve various CLDs' diagnosis in the early stage, thereby achieving targeted treatment and increasing the potential and value of clinical applications.