Lung cancer is the leading cause of death for men and women worldwide and the second most frequent cancer. Therefore, early detection of the disease increases the cure rate. This paper presents a new approach to evaluate the ability of positron emission tomography/computed tomography (PET/CT) images to classify and detect lung cancer using deep learning techniques. Our approach aims to fully automate lung cancer's anatomical localization from PET/CT images. It also searches to classify the tumor, which is essential as it makes it possible to determine the disease's speed of progression and the best treatments to adopt. We have built, in this work, an approach based on transformers by implementing the DETR model as a tool to detect the tumor and assist physicians in staging patients with lung cancer. The TNM staging system and histologic subtype classification were both taken as a standard for classification. Experimental results demonstrated that our approach achieves sound results on tumor localization, T staging, and histology classification. Our proposed approach detects tumors with an intersection over union (IOU) of 0.8 when tested on the Lung-PET-CT-Dx dataset. It also has yielded better accuracy than state-of-the-art T-staging and histologic classification methods. It classified T-stage and histologic subtypes with an accuracy of 0.97 and 0.94, respectively.