TAS-102 in Previously Treated Unresectable or Metastatic Squamous Cell Lung Carcinoma (UF-STO-LUNG-003)

Inclusion Criteria: * Those who will be eligible will be all patients with unresectable and/or metastatic squamous cell non-small cell lung cancer who have disease which has been previously treated with an Food \& Drug Administration (FDA)- or National Comprehensive Cancer Network (NCCN)-approved platinum doublet. Patients who have not received such therapy must have medical reasons for not receiving such therapy. Those who have a molecularly targetable genetic mutation in their tumor must have also received the appropriate specific therapy for that mutation. All will be appropriate candidates for chemotherapy treatment. Subjects must meet all of the additional following criteria to be eligible for study participation: * Eastern Cooperative Oncology Group (ECOG) Performance Status \<2 * Life expectancy \> 12 weeks * Male or female' age \>18 years * Patients of childbearing potential must be using an effective means of contraception. * Histologic diagnosis of squamous non-small cell lung cancer that has been treated adequately in the metastatic or unresectable setting with a platinum doublet chemotherapy regimen and now has evidence of disease progression. Patients may have also received additional chemotherapy, such as an immune checkpoint inhibitor or no more than one additional cytotoxic agent (thus participants may have received between one to three prior lines of therapy for metastatic or unresectable disease). * Patients who have received platinum-based doublet therapy in the neoadjuvant or adjuvant setting will only be eligible if they have experienced disease progression after their last dose of cytotoxic chemotherapy. * Patients who have a neoplasm for which there currently exists an FDA-approved targeted therapy (such as to epidermal growth factor receptor \[EGFR\] activating mutations, or ALK or ROS1 gene rearrangements) must have received all such targeted therapies and either exhibited progressive disease through such treatments, or have been shown to be intolerant of such therapies, prior to enrollment on this study. * Baseline laboratory values (bone marrow, renal, hepatic): * Adequate bone marrow function: * Absolute neutrophil count \>1000/µL * Platelet count \>100'000/µL * Renal function: * Serum creatinine \< 2.0 mg/dL * Hepatic function: * Bilirubin \<1.5x upper limit of normal (ULN) * Serum calcium \< 12 mg/dL * Women of childbearing potential (WOCBP) must be using an adequate method of contraception to avoid pregnancy throughout the study and for at least 6 months after the last dose of study drug to minimize the risk of pregnancy. Prior to study enrollment, women of childbearing potential must be advised of the importance of avoiding pregnancy during trial participation and the potential risk factors for an unintentional pregnancy. WOCBP include any woman who has experienced menarche and who has not undergone successful surgical sterilization (hysterectomy, bilateral tubal ligation, or bilateral oophorectomy) or who is not post-menopausal. Post-menopause is defined as: * Amenorrhea that has lasted for ≥ 12 consecutive months without another cause, or * For women with irregular menstrual periods who are taking hormone replacement therapy (HRT), a documented serum follicle-stimulating hormone (FSH) level of greater than 35 mIU/mL. * Males with female partners of child-bearing potential must agree to use physician-approved contraceptive methods (e.g., abstinence, condoms, vasectomy) throughout the study and should avoid conceiving children for 3 months following the last dose of study drug. * Subjects must have provided written informed consent and be willing to comply with all study-related procedures. Exclusion Criteria: * Pregnant or lactating females * Patients with a mixed histology NSCLC, such as adenosquamous carcinoma, where the squamous component is \<50% of the assessed lesion * Patients with a mixed histology where there are any small cell elements * Patients who have not received and progressed through, refused, or been intolerant of, a commonly utilized platinum-doublet therapy (cisplatin or carboplatin paired with docetaxel, paclitaxel, nab-paclitaxel, gemcitabine, vinorelbine, etoposide or irinotecan) administered for the treatment of unresectable or metastatic lung cancer. * Patients who have not received the appropriate prior targeted therapy for their lung cancer if eligible * Any invasive malignancy treated within 3 years prior to Cycle 1, Day 1 * Myocardial infarction or ischemia within the 6 months before Cycle 1' Day 1 * Uncontrolled' clinically significant dysrhythmia, or prolonged QT segment * Uncontrolled malignant disease in the central nervous system (previously treated disease is eligible, provided it has been radiographically stable for at least four weeks) * Radiotherapy within the 2 weeks before Cycle 1, Day 1. If any radiation has been administered to the target lesion there must be evidence of growth by radiographic assessments or physical examination * Major surgery within the 2 weeks before Cycle 1, Day 1 * Any co morbid condition that' in the view of the attending physician' renders the patient at high risk from treatment complications * Subjects unwilling to use an acceptable method to avoid pregnancy for the entire study period and for at least 24 weeks after the last dose of study drug. * History of any other disease, metabolic dysfunction, physical examination finding, or clinical laboratory finding giving reasonable suspicion of a disease or condition that contraindicates the use of protocol therapy or that might affect the interpretation of the results of the study or that puts the subject at high risk for treatment complications, in the opinion of the treating physician. * Prisoners or subjects who are involuntarily incarcerated. * Subjects who are compulsorily detained for treatment of either a psychiatric or physical illness. * Subjects demonstrating an inability to comply with the study and/or follow-up procedures.