Lung cancer is a leading global cause of cancer mortality and histopathological analysis is the criterion standard for diagnosis. Accurate typing of lung cancer histology types, such as lung adenocarcinoma and lung squamous cell carcinoma, and differential diagnosis from benign tissue are critical to ideal clinical decision-making and treatment planning. In this paper, we present DeepHist, a deep histopathological lung tissue image classifier for multi-class histopathological lung tissue classification. We utilized 15,000 high-resolution images equally distributed into three classes (lung benign tissue, lung adenocarcinoma, and lung squamous cell carcinoma) of a public Kaggle dataset. We performed extensive experiments with some of the existing state-of-the-art convolutional neural network architectures, i.e., VGG19, InceptionV3, ConvNeXtBase, ResNet50V2, and DenseNet169 (salinity-augmented). Of the three, ResNet50V2, and DenseNet169 performed best with precision, recall, and F1 being 0.99 for each of them. These findings indicate deep learning models can potentially automate histopathological assessment to near-human level. Our study indicates it is conceivable to use deep learning techniques as adjunct diagnostic aids to aid pathologists to differentiate between lung cancer types and potentially improve efficiency in diagnosis and reduce subjectivity. Follow-up studies may involve explainability methods and clinical validation.