Temozolomide With or Without Veliparib in Treating Patients With Relapsed or Refractory Small Cell Lung Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed small cell lung cancer; confirmation will be done at Memorial Sloan-Kettering Cancer Center (MSKCC) or locally for participating sites * Patients' disease has relapsed or progressed after one or two prior chemotherapy regimens, one of which must have been an etoposide-platinum doublet; eligible patients will be defined as follows: * "Sensitive" disease: patients who had one previous line of chemotherapy and maintained an appropriate response for \> 60 days * "Refractory" disease: those patients with either (a) no response to first-line chemotherapy or progression =\< 60 days after completing treatment, or (b) "sensitive" or "refractory" disease in need of third-line therapy (i.e. completed or failed two previous lines of chemotherapy) * Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 (Karnofsky \>= 70%) * Patients with asymptomatic brain metastases that do not require immediate whole brain radiation therapy and are on stable doses of steroids are allowed * Patients must have measurable disease, which is defined as at least one lesion that can be accurately measured in at least one dimension on a computed tomography (CT) scan as per RECIST version 1.1; brain metastases can be considered measurable disease if they meet this criterion * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Hemoglobin \>= 8.5 g/dL; the use of transfusion to achieve this crit…