Lung cancer is recognized as the most life-threatening cancer among other type of cancers all over the world. Early stage recognition and proper diagnosis can increase the five-year survival rate and also save the patient life. Accurate identification of lung cancer subtype from histopathological images plays an important role and help doctors to take necessary decisions for lung cancer treatment. Therefore, in this work, a new deep learning (DL) framework based on image morphology is developed for lung cancer subtype classification. The proposed Morphology-based Attention Network, (MorphAttnNet) can classify lung benign, adenocarcinoma (ADC), and squamous cell carcinoma (SCC) from histopathology images. The framework is designed based on convolution and morphological operations. Attention-based mechanism is incorporated to select important features from histopathology images. The framework with its morphology-based path combined with attention blocks is able to capture morphological variations of lung cancer subtypes accurately and effectively. Finally, the extracted deep features from convolution and morphological paths are combined and used for lung cancer subtype classification. The performance of the proposed framework is analyzed on publicly available LC25000 dataset and achieved a sensitivity, specificity, average accuracy, precision, and f1-score of 98.33%, 97.76%, 98.96%, 99.12%, and 98.72% respectively for lung cancer subtype classification. The proposed system is also compared with existing state-of-the-art systems and achieved considerable performance indices for lung cancer subtype classification.