Lung diseases are one of the primary causes of mortality worldwide. The majority of lung disorders are not discovered until they have progressed significantly. Computer Aided Diagnosis (CADx) systems allow for immediate and earlier diagnosis and are being expanded. This study investigates the feasibility of employing methods for learning features from fine-tuned adaptive learning rate Deep Learning (DL) architectures to provide robust and comprehensive features on the NIH Chest X-ray Dataset for three classes (Cardiomegaly, Emphysema, and Hernia) lung disease. A novel dual feature extraction using residual networks with a nature-inspired Gray Wolf Optimization (GWO) algorithm and Deep Dense Neural Network (ResNet-GWO-DD) is proposed in this study. Dual feature extraction is experimented with using two fine-tuned ResNet-50 and ResNet-101 Transfer Learning (TL) architectures. The global best optimal extracted features were optimized using GWO and are further combined for classification using a Deep Dense Neural Network. The dual learning of deep features using ResNet-50 and ResNet-101 helps the GWO to learn the global best optimal features. These dual learning capabilities greatly enhance the performance of the proposed model and achieve significant accuracy while comparing the state-of-the-art methods. The performance of the proposed method is further evaluated using three different optimizers such as Adam, Stochastic Gradient Descent (SGD), and Continuous Coin Betting (COCOB). Deep features extracted using GWO and optimizer Adam have yielded maximum accuracy of 99.68%, 96.63%, and 96.58% for Hernia, Emphysema, and Cardiomegaly respectively compared to SGD and COCOB.