This is a non-randomized, open label, sequentially enrolling phase II study with a Simon two-step enrollment design to evaluate the activity of TAS-102 in previously treated unresectable or metastatic squamous non-small cell cancer after progression through or intolerance to prior systemic therapy. The trial therapy of TAS-102 is to be administered orally at 35 mg/m2 each dose twice daily. The primary objective of the trial is to determine the progression-free survival, in months, of subjects receiving TAS 102 for the treatment of unresectable or metastatic recurrent squamous non-small cell lung cancers.