The use of deep learning (DL) in medical image analysis has significantly improved the ability to predict lung cancer. In this study, we introduce a novel deep convolutional neural network (CNN) model, named ResNet+, which is based on the established ResNet framework. This model is specifically designed to improve the prediction of lung cancer and diseases using the images. To address the challenge of missing feature information that occurs during the downsampling process in CNNs, we integrate the ResNet-D module, a variant designed to enhance feature extraction capabilities by modifying the downsampling layers, into the traditional ResNet model. Furthermore, a convolutional attention module was incorporated into the bottleneck layers to enhance model generalization by allowing the network to focus on relevant regions of the input images. We evaluated the proposed model using five public datasets, comprising lung cancer (LC2500 $n$=3183, IQ-OTH/NCCD $n$=1336, and LCC $n$=25000 images) and lung disease (ChestXray $n$=5856, and COVIDx-CT $n$=425024 images). To address class imbalance, we used data augmentation techniques to artificially increase the representation of underrepresented classes in the training dataset. The experimental results show that ResNet+ model demonstrated remarkable accuracy/F1, reaching 98.14/98.14\% on the LC25000 dataset and 99.25/99.13\% on the IQ-OTH/NCCD dataset. Furthermore, the ResNet+ model saved computational cost compared to the original ResNet series in predicting lung cancer images. The proposed model outperformed the baseline models on publicly available datasets, achieving better performance metrics. Our codes are publicly available at https://github.com/AIPMLab/Graduation-2024/tree/main/Peng.