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 criterion should be at the discretion of the investigators * Total bilirubin =\< 1.5 mg/dL x institutional upper limit of normal * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3.0 x institutional upper limit of normal * Creatinine =\< 1.5 x institutional upper limit of normal OR creatinine clearance \>= 50 mL/min/1.73 m\^2 for patients with creatinine levels \>= 1.5 x upper limit of institutional normal * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * For women of child-bearing potential, negative pregnancy test within 14 days prior to starting temozolomide and ABT-888 * Ability to understand and the willingness to sign a written informed consent document * Able to swallow pills * Patients will not be excluded based on the diagnosis of acquired immune deficiency syndrome (AIDS); given the increased risk of infection, these patients should have cluster of differentiation (CD)4 counts above 200 cells/mm\^3; patients with AIDS or human immunodeficiency virus (HIV) not receiving agents with the potential for pharmacokinetic interactions with ABT-888 may be eligible Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 3 weeks prior to entering the study * Patients who have not recovered from adverse events due to agents administered more than 3 weeks earlier; toxicities should have resolved to baseline or to within one grade level of their baseline (not to exceed grade 2) * Patients who have been administered ABT-888, any other PARP-inhibitor, or temozolomide * Patients may not be receiving any other investigational agents * Patients with leptomeningeal involvement * Patients with active seizures or a history of seizures * History of allergic reactions attributed to compounds of similar chemical or biologic composition to ABT-888 or temozolomide * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with ABT-888; these potential risks also apply to temozolomide * Patients with either AIDS or HIV on combination antiretroviral therapy are ineligible * Patients with a synchronous active malignancy requiring treatment