Lung and Colorectal (LC) cancer is life-threatening and rapidly developing cancers. According to World Health Organization (WHO), approximately 4.14 million lung and colorectal cancer cases were newly diagnosed, with 2.7 million fatalities. An International Agency for Research on Cancer (IARC) reported that there will be more than 3 million additional instances of colorectal cancer worldwide between 2020 and 2040. Early diagnosis of LC cancer is very helpful for treatment and can save the precious human life. The conventional diagnosis methods are expensive and time consuming. In this work, we present an accurate and efficient model for the classification of Lung and Colorectal (LC) cancer. We utilize two well-known pre-trained deep learning models, ResNet50 and EfficientNetB0, and fine-tuned the both models based on the addition and removal of layers. After the fine-tuning, manual hit and trail based hyperparameters are initialized. Later on, the deep transfer learning was performed and obtained the trained models. Two different feature vectors have been extracted from both models and fused using a priority based serial approach. To further improve the performance of extracted features, Normal Distribution based Gray Wolf Optimization algorithm is employed and obtained the best features that given as input to five classifiers. The output of these five classifiers is then utilized by soft voting technique to generate the final prediction. Experimental results show that the proposed architecture achieved an overall 98.73% accuracy on LC25000 dataset. Furthermore, prediction time was reduced by 19.14%. Comparison with the state-of-the-art techniques shows that the proposed technique obtained the improved performance results.