Chemotherapy With or Without Bevacizumab in Treating Patients With Stage IB, Stage II, or Stage IIIA Non-small Cell Lung Cancer That Was Removed By Surgery

Inclusion Criteria:

* In order to be eligible for this trial, patients must have undergone complete resection of their non-small cell lung cancer (NSCLC) \[stage IB (\>= 4 cm)\] - \[IIIA (T2-3N0, T1-3N1, T1-3N2\] prior to enrollment; accepted types of resection will consist of lobectomy, sleeve lobectomy, bi-lobectomy or pneumonectomy; resections by segmentectomy or wedge resection will not be accepted; mediastinal lymph node sampling at specified levels is required pre-operatively (mediastinoscopy) or intraoperatively (level 7 and 4 for right sided tumors or level 7 and 5 and/or 6 for left sided tumors)
* Patients must be no less than 6 weeks (42 days) and no more than 12 weeks (84 days) post-thoracotomy at the time of randomization and must be adequately recovered from surgery
* Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1
* Patients must not have received the following:

  * Prior systemic chemotherapy at any time; methotrexate (MTX) given in low doses for non-malignant conditions with last dose at least 2 weeks prior to date of registration will be allowed; other low dose chemotherapeutics for non-malignant conditions will be considered, but review by the study chair is required
  * Hormonal cancer therapy or radiation therapy as prior cancer treatment within 5 years of randomization; (prior surgery, biologic therapy, hormonal therapy, or radiation therapy for a malignancy over 5 years prior to enrollment that is now considered cured is acceptable)
* Patients must not have any history of cancer within 5 years from randomization, with the exception of in-situ carcinoma of the cervix or completely resected non-melanoma skin cancer
* Absolute neutrophil count (ANC) \>= 1500 mm\^3
* Platelets \>= 100,000/mm\^3
* Prothrombin time/international normalized ratio (INR) =\< 1.5

  * Or, if patient is on therapeutic anticoagulation, prothrombin time/INR =\< 3.0
* Partial thromboplastin time (PTT) =\< institutional upper limit of normal (ULN) OR, if patient is on therapeutic anticoagulation, PTT must be =\< 1.5 x ULN
* Total bilirubin =\< 1.5 mg/dL
* Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) \< 5 x upper limit of normal (ULN)
* Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) \< 5 x upper limit of normal (ULN)
* Serum creatinine =\< 1.5 x institutional upper limit of normal (ULN)
* Urine protein should be screened by urine analysis for urine protein creatinine (UPC) ratio; for UPC ratio \> 0.5, 24-hour urine protein must be obtained and the level must be \< 1000 mg (1 g) for patient enrollment
* Patients with a known history of myocardial infarction or other evidence of arterial thrombotic disease (angina) will be allowed on study only if they have had no evidence of active disease for at least 12 months prior to randomization
* Patients with any history of cerebral vascular accident (CVA) or transient ischemic attack (TIA) will not be allowed on trial
* Women must not be pregnant or breast-feeding

  * All females of childbearing potential must have a blood or urine test within 2 weeks prior to randomization to rule out pregnancy
* Both fertile men and women must agree to use adequate contraceptive measures during study treatment and for at least 6 months after completion of bevacizumab
* Patients must not have any clinically significant ongoing, active or serious infection, symptomatic or uncontrolled congestive heart failure, symptomatic or uncontrolled cardiac arrhythmia or any other medical condition or psychiatric illness/social situations that would limit compliance with study requirements
* Patients must have no history of bleeding diathesis or coagulopathy
* All patients must have a documented blood pressure (BP) with systolic =\< 150 and diastolic =\< 90 within 28 days of registration; patients with known hypertension must be on a stable regimen of anti-hypertensive therapy
* Patients receiving daily treatment with aspirin or non-steroidal anti-inflammatory agents (NSAIDS) are eligible; treatment with dipyridamole (Persantine), ticlopine (Ticlid), clopidogrel (Plavix) and/or cilostazol (Pletal) is not allowed; patients must have stopped taking any of these agents at least 7 days prior to randomization
* Patients must not have serious non-healing wound, ulcer, bone fracture, or have undergone a major surgical procedure, open biopsy, or significant traumatic injury within 28 days prior to randomization OR core biopsy within 7 days prior to randomization
* Patients must not have a history of abdominal fistula, gastrointestinal perforation or intra-abdominal abscess within 28 days prior to randomization
* Patients must not have any anticipated major surgical procedure(s) during the course of the study
* Patients must not have known hypersensitivity to Chinese hamster ovary cell products or other recombinant human antibodies
* Patients may be on a stable regimen of therapeutic anticoagulation or may be receiving prophylactic anticoagulation of venous access devices, provided that coagulation studies meet entry criteria above; caution must be exercised for patients requiring anticoagulation, including treatment with low dose heparin or low molecular weight heparin for deep vein thrombosis (DVT) prophylaxis while on study
* Patients with ongoing post-operative hemoptysis (defined as bright red blood of 1/2 teaspoon or more) are not eligible; patients with pre-operative hemoptysis that has resolved post-operatively are eligible
* Patients who will receive pemetrexed (pemetrexed disodium)/cisplatin therapy must also meet the following criteria:

  * Patients assigned to pemetrexed/cisplatin therapy must NOT have squamous cell histology
  * Calculated creatinine clearance must be obtained within 2 weeks of randomization and calculated creatinine clearance (CrCl) must be \>= 45 mL/min using the standard Cockcroft and Gault formula, or the measured glomerular filtration rate (GFR) using the appropriate radiolabeled method (\[51\]chromium-labeled ethylenediaminetetraacetic acid \[51-CrEDTA\] or technetium 99m diethylenetriamine-pentaacetic acid \[Tc99m-DTPA\]) must be used to calculate CrCl