Dasatinib in Treating Patients With Relapsed Small Cell Lung Cancer

Inclusion Criteria: * Histologically or cytologically confirmed small cell lung cancer (SCLC) (limited or extensive stage disease) * Progressive or recurrent disease after an initial response to first-line treatment with a platinum-based chemotherapy with or without concurrent definitive radiotherapy to the chest (chemotherapy must have been completed at least 90 days prior to documentation of relapse) * Measurable disease, defined as \>= 1 unidimensionally measurable lesion \>= 20 mm by conventional techniques OR \>= 10 mm by spiral CT scan * Lesions that are not considered measurable include the following: * Bone lesions * Leptomeningeal disease * Ascites * Pleural or pericardial effusion * Abdominal masses that are not confirmed and followed by imaging techniques * Cystic lesions * Tumor lesions situated in a previously irradiated area, unless progression after radiotherapy is documented in these lesions * No known brain metastases (previously treated brain metastases allowed provided they are neurologically stable for \>= 4 weeks) * ECOG performance status 0-1 * Platelet count \>= 100,000/mm\^3 * Bilirubin =\< 1.5 times upper limit of normal (ULN) * Creatinine =\< 1.5 times ULN OR creatinine clearance \>= 60 mL/min * AST =\< 2.5 times ULN * Not pregnant or nursing * Negative pregnancy test * No significant cardiac disease, including any of the following: * New York Heart Association class III-IV heart disease * Myocardial infarction or ventricular tachyarrhythmia within the past 6 months * Prolonged QTc \> 480 msec (Fridericia correction) * Major conduction abnormality (unless a cardiac pacemaker is present) * No more than 1 prior chemotherapy regimen * No prior dasatinib or compounds of similar chemical composition or similar biologic therapeutic activity including, but not limited to, any inhibitors of SRC, BCR-ABL, c-KIT, EPHA2, or PDGFRB kinases * At least 2 weeks since prior definitive or palliative radiotherapy (prior radiotherapy allowed in the context of combined modality treatment with curative intent for limited stage disease; prophylactic cranial radiotherapy; or palliative radiotherapy initially or at relapse) * At least 2 weeks since prior surgery and recovered * At least 1 week since prior and no concurrent agents with proarrhythmic potential * At least 1 week since prior and no concurrent CYP3A4 inhibitors or inducers * At least 1 week since prior and no concurrent grapefruit concentrate * No concurrent palliative radiotherapy * No concurrent hormones or other chemotherapeutic agents, except steroids for adrenal failure, hormones for noncancer-related conditions (e.g., insulin for diabetes), or intermittent dexamethasone as an antiemetic * No concurrent combination antiretroviral therapy for HIV-positive patients * No other concurrent chemotherapeutic or investigational agents * Fertile patients must use effective contraception during and for \>= 6 weeks after completion of study therapy