Early detection of lung cancer is critical to improving survival outcomes. We present a deep learning framework for automated lung cancer screening from chest computed tomography (CT) images with integrated explainability. Using the IQ-OTH/NCCD dataset (1,197 scans across Normal, Benign, and Malignant classes), we evaluate a custom convolutional neural network (CNN) and three fine-tuned transfer learning backbones: DenseNet121, ResNet152, and VGG19. Models are trained with cost-sensitive learning to mitigate class imbalance and evaluated via accuracy, precision, recall, F1-score, and ROC-AUC. While ResNet152 achieved the highest accuracy (97.3%), DenseNet121 provided the best overall balance in precision, recall, and F1 (up to 92%, 90%, 91%, respectively). We further apply Shapley Additive Explanations (SHAP) to visualize evidence contributing to predictions, improving clinical transparency. Results indicate that CNN-based approaches augmented with explainability can provide fast, accurate, and interpretable support for lung cancer screening, particularly in resource-limited settings.