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The purpose of this study is to: * Test how well the study medicine Abemaciclib, a CDK4/6 inhibitor, works to shrink lung cancer tumors in the body. * Test the safety of Abemaciclib when given to participants with small cell lung cancer (SCLC), large cell neuroendocrine lung cancer, extrapulmonary small cell cancers and other high grade neuroendocrine cancers of the lung. Specifically, this study is looking at SCLC, large cell neuroendocrine lung cancer, extrapulmonary small cell cancers and other high grade neuroendocrine cancers of the lung that have not responded to treatment (refractory) or come back after treatment with chemotherapy (relapsed) as the study medication has been shown to be effective any time the disease relapses not just in the first few months.