This is a phase 1, single-center, open-label study that enrolls adult subjects with extensive stage lung cancer or stage IV non-small cell lung cancer that is platinum-refractory and received PD-1 and/or PD-L1 therapy. The purpose of this study is to test the safety of using a new treatment called autologous T lymphocyte chimeric antigen receptor cells against the GD2 antigen (iC9-GD2.CAR.IL-15 T cells) in subjects with lung cancer. How much (dose) of the iC9-GD2.CAR.IL-15 T cells are safe to use without causing too many side effects and what is the maximum dose that could be tolerated will be studied. Modified immune cells as an experimental treatment that combines antibodies and T cells will be used. Antibodies are proteins that protect the body from foreign invaders like bacteria. T cells, also called T lymphocytes, are special infection-fighting blood cells that can kill viruses and other cells, including tumor cells. Although antibodies and T cells have been used to treat cancer and they both have shown promise, neither alone has been able to cure most patients. This study will combine T cells and antibodies to create a more effective treatment. The treatment that is being researched in this study is called autologous T lymphocyte chimeric antigen receptor cells targeted against the disialoganglioside (GD2) antigen that expresses Interleukin (IL)-15, and the inducible caspase 9 safety switch (iC9). The short name for this treatment is iC9.GD2.CAR.IL-15 T cells therapy is an experimental therapy and has not been approved by the Food and Drug Administration. There are two steps. In the first step, blood will be collected from the subjects to prepare the iC9-GD2.CAR.IL-15 T cells. T cells will be isolated from the blood and modified to make iC9-GD2.CAR.IL-15. In the second step, the iC9-GD2.CAR.IL-15 T cells produced from the subject's own blood will be administered to the subject.