Lumpy Skin Disease (LSD) is a contagious viral infection that significantly deteriorates livestock health, thereby posing a serious threat to the global economy and food security. Owing to its rapid spread characteristics, early and precise identification is crucial to prevent outbreaks and ensure timely intervention. In this paper, we propose a hybrid deep learning-based approach called LUMPNet for the early detection of LSD. LUMPNet utilizes image data to detect and classify skin nodules -- the primary indicator of LSD. To this end, LUMPNet uses YOLOv11, EfficientNet-based CNN classifier with compound scaling, and a novel adaptive hybrid optimizer. More precisely, LUMPNet detects and localizes LSD skin nodules and lesions on cattle images. It exploits EfficientNet to classify the localized cattle images into LSD-affected or healthy categories. To stabilize and accelerate the training of YOLOv11 and EfficientNet hybrid model, a novel adaptive hybrid optimizer is proposed and utilized. We evaluate LUMPNet at various stages of LSD using a publicly available dataset. Results indicate that the proposed scheme achieves 99% LSD detection training accuracy, and outperforms existing schemes. The model also achieves validation accuracy of 98%. Moreover, for further evaluation, we conduct a case study using an optimized EfficientNet-B0 model trained with the AdamW optimizer, and compare its performance with LUMPNet. The results show that LUMPNet achieves superior performance.