This trial tests a combination of two drugs, afatinib and prednisone, for patients with advanced squamous non-small cell lung cancer. Afatinib aims to stop cancer growth by targeting specific proteins, while prednisone helps reduce inflammation and immune reactions. The goal is to find out if this combination is safe and effective for these patients. Afatinib has been shown to be effective as a follow-up treatment for advanced lung squamous cell carcinoma and has benefits in combination with other therapies.