Lung squamous cell carcinoma in situ (SCIS) is the preinvasive precursor lesion of lung squamous cell carcinoma (SCC). Only around two-thirds of these lesions progress to invasive cancer, while one-third undergo spontaneous regression, which presents a significant clinical challenge due to the risk of overtreatment. The ability to predict the evolution of SCIS lesions can significantly impact patient management. Our study explores the use of computational pathology in predicting the evolution of SCIS. We used a dataset consisting of 112 H&E-stained whole slide images (WSIs) that were obtained from the Image Data Resource public repository. The dataset corresponded to tumors of patients who underwent biopsies of SCIS lesions and were subsequently followed up by bronchoscopy and CT scans to monitor for progression to SCC. We used this dataset to train two models: a pathomics-based ridge classifier trained on 80 principal components derived from almost 2000 extracted features and a deep convolutional neural network with a modified ResNet18 architecture. The performance of both approaches in predicting progression was assessed. The pathomics-based ridge classifier model obtained an F1-score of 0.77, precision of 0.80, and recall of 0.77. The deep learning model performance was similar, with a WSI-level F1-score of 0.80, precision of 0.71, and recall of 0.90. These findings highlight the potential of computational pathology approaches in providing insights into the evolution of SCIS. Larger datasets will be required in order to train highly accurate models. In the future, computational pathology could be used in predicting outcomes in other preinvasive lesions.