Prognosis prediction is crucial for determining optimal treatment plans for lung cancer patients. Traditionally, such predictions relied on models developed from retrospective patient data. Recently, large language models (LLMs) have gained attention for their ability to process and generate text based on extensive learned knowledge. In this study, we evaluate the potential of GPT-4o mini and GPT-3.5 in predicting the prognosis of lung cancer patients. We collected two prognosis datasets, i.e., survival and post-operative complication datasets, and designed multiple tasks to assess the models' performance comprehensively. Logistic regression models were also developed as baselines for comparison. The experimental results demonstrate that LLMs can achieve competitive, and in some tasks superior, performance in lung cancer prognosis prediction compared to data-driven logistic regression models despite not using additional patient data. These findings suggest that LLMs can be effective tools for prognosis prediction in lung cancer, particularly when patient data is limited or unavailable.