Veliparib With or Without Radiation Therapy, Carboplatin, and Paclitaxel in Patients With Stage III Non-small Cell Lung Cancer That Cannot Be Removed by Surgery

Inclusion Criteria:

* Patients must have histologically or cytologically-proven new diagnosis of unresectable stage IIIA/IIIB\*, non-small cell lung cancer (adenocarcinoma, bronchioloalveolar cell carcinoma, large cell carcinoma, squamous cell carcinoma, or mixed)

  * Per the American Joint Committee on Cancer (AJCC) 7th edition, pleural and pericardial are now considered stage M1a disease; when pleural fluid is visible on the computed tomography (CT) scan or on a chest x-ray, a thoracentesis is required to confirm that the pleural fluid is cytologically negative; patients with exudative pleural effusions are excluded, regardless of cytology; patients with effusions that are minimal (i.e. not visible on chest x-ray) that are too small to safely tap are eligible; a small effusion that has positive fludeoxyglucose F 18 (FDG) uptake on positron emission tomography (PET) has to be proven to be malignant per standard of care diagnostic procedures for the patient to be excluded
* Patients must have measurable or non-measurable disease documented by CT, magnetic resonance imaging (MRI) or PET/CT; the CT from a combined PET/CT may be used to document only non-measurable disease unless the scan is of diagnostic quality; measurable disease must be assessed by CT within 28 days prior to registration; pleural effusions, ascites and laboratory parameters are not acceptable as the only evidence of disease; non-measurable disease must be assessed within 42 days prior to registration; all disease must be assessed and documented on the Baseline Tumor Assessment Form
* Patients with brain metastases are ineligible; all patients must have a pretreatment CT or MRI scan of the brain to evaluate for central nervous system (CNS) disease within 42 days prior to registration
* Patients must not have received any prior systemic therapy (chemotherapy or other biologic therapy) for lung cancer
* Patients must not have received prior chest radiation therapy for NSCLC
* Patients must not have had a previous surgical resection; however, patients may have undergone exploratory thoracotomy, mediastinoscopy, excisional biopsy or similar surgery for the purpose of determining the diagnosis, stage or potential resectability of newly diagnosed lung tumor; at least 28 days must have elapsed since thoracic surgery (excluding mediastinoscopy or other minor surgeries) and patients should have recovered from all associated toxicities at the time of registration; patients must not be planning to undergo a minor surgical procedure while on this study
* Patients must have Zubrod performance status 0-1
* Patients must have tumor tissue available for submission to assess gene expression of ERCC1 and XRCC1; patients must also be offered participation in banking for future use of specimens
* Absolute neutrophil count \>= 1,500/mcl
* Platelets \>= 100,000/mcl
* Hemoglobin \>= 9.0 g/dl
* Total bilirubin within institutional upper limit of normal (IULN)
* Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) or serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 2.5 x IULN
* Patients must not be pregnant or nursing; women/men of reproductive potential must have agreed to use an effective contraceptive method; a woman is considered to be of "reproductive potential" if she has had menses at any time in the preceding 12 consecutive months; in addition to routine contraceptive methods, "effective contraception" also includes heterosexual celibacy and surgery intended to prevent pregnancy (or with a side-effect of pregnancy prevention) defined as a hysterectomy, bilateral oophorectomy or bilateral tubal ligation; however, if at any point a previously celibate patient chooses to become heterosexually active during the time period for use of contraceptive measures outlined in the protocol, he/she is responsible for beginning contraceptive measures
* Patients must have a serum creatinine =\< the IULN AND measured or calculated creatinine clearance \>= 60 cc/min using the Cockroft-Gault formula
* Patients must have pulmonary function tests (PFTs) including forced expiratory volume in 1 second (FEV1) within 84 days prior to registration; for FEV1, the best value obtained pre- or post-bronchodilator must be \>= 1.2 liters/second and/or \>= 50% predicted
* Patients may not be planning to receive any other investigational agents
* Patients must not have more than 10% weight loss in the past 6 months
* Patients must not have a history of allergic reactions attributed to compounds of similar chemical or biologic composition to ABT-888, carboplatin, paclitaxel or other agents used in study
* No other prior malignancy is allowed except for the following: adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, adequately treated stage I or II cancer from which the patient is currently in complete remission, or any other cancer from which the patient has been disease free for five years
* Patient must not have any 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
* Patients must not currently have a \> grade 1 symptomatic neuropathy-sensory (National Cancer Institute \[NCI\] Common Terminology Criteria for Adverse Events \[CTCAE\] version 4.0)
* Patients must not have a history of seizures
* Patients must not have any known immune deficiencies; patients with immune deficiency are at increased risk of lethal infections when treated with marrow-suppressive therapy; therefore, known human immunodeficiency virus (HIV) positive patients receiving combination anti-retroviral therapy are excluded from the study
* Patients must be able to swallow whole capsules
* Prestudy history and physical must be obtained within 28 days prior to registration
* All patients must be informed of the investigational nature of this study and must sign and give written informed consent in accordance with institutional and federal guidelines
* As a part of the Oncology Patient Enrollment Network (OPEN) registration process the treating institution's identity is provided in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered in the system
* REGISTRATION #2 - PRIOR TO CONSOLIDATION CHEMOTHERAPY:
* REGISTRATION #2 - PRIOR TO CONSOLIDATION CHEMOTHERAPY: Patients must have completed chemoradiotherapy per protocol and at least four weeks but no more than six weeks must have elapsed from the last day of induction therapy (the last day of radiation)
* REGISTRATION #2 - PRIOR TO CONSOLIDATION CHEMOTHERAPY: Patients must have undergone restaging tests according to the study calendar and determined to have no evidence of disease progression
* REGISTRATION #2 - PRIOR TO CONSOLIDATION CHEMOTHERAPY: Patients must have a serum creatinine =\< (IULN) AND measured of calculated creatinine clearance \>= 60 cc/min using the Cockroft-Gault formula
* REGISTRATION #2 - PRIOR TO CONSOLIDATION CHEMOTHERAPY: Absolute neutrophil count \>= 1,500 mcl
* REGISTRATION #2 - PRIOR TO CONSOLIDATION CHEMOTHERAPY: Platelets \>= 100,000/mcl
* REGISTRATION #2 - PRIOR TO CONSOLIDATION CHEMOTHERAPY: Hemoglobin \>= 9.0 g/dl
* REGISTRATION #2 - PRIOR TO CONSOLIDATION CHEMOTHERAPY: Total bilirubin =\< IULN
* REGISTRATION #2 - PRIOR TO CONSOLIDATION CHEMOTHERAPY: SGOT (AST) or SGPT (ALT) =\< 2.5 x IULN
* REGISTRATION #2 - PRIOR TO CONSOLIDATION CHEMOTHERAPY: Patients must have Zubrod performance status 0-1