Carboplatin, Paclitaxel, and Bevacizumab With or Without Erlotinib Hydrochloride in Treating Non-Smokers With Advanced Non-Small Cell Lung Cancer

Inclusion Criteria: * Measurable disease as defined by Response Criteria In Solid Tumors (RECIST) criteria * Baseline measurements and evaluations of all sites of disease must be obtained =\< 4 weeks (28 days) prior to randomization * Eastern Cooperative Oncology Group (ECOG) performance status between 0-1 * No prior chemotherapy for lung cancer; prior chemotherapy for an unrelated condition is allowed if completed \> 3 years prior to date of randomization * Histological or cytologic evidence of non-small cell lung cancer * Patients must not have any additional active, invasive malignancies requiring therapy * Patients must have smoked less than or equal to 100 cigarettes in their lifetime * Stage IV or IIIB (with pleural or pericardial effusion or multifocal pleural involvement) or recurrence after prior curative resection or definitive radiation * Prior radiation therapy (RT) is allowed, provided RT has ended at least 2 weeks (14 days) prior to date of randomization; patients must have recovered from any adverse events related to the RT (except alopecia and grade 1 neuropathy); no previous irradiation to the only site of measurable disease, unless that site has had subsequent evidence of pathologic or radiologic progression * Absolute neutrophil count (ANC) \>= 1500/mm\^3 * Platelet count \>= 100,000/mm\^3 * Bilirubin =\< 1.5 mg/dl * Creatinine =\< 2.0 mg/dl * Serum glutamic oxaloacetic transaminase (SGOT) and serum glutamic pyruvate transaminase (SGPT) =\< 3 X institutional upper limit of normal (ULN) * Women must not be pregnant or breast-feeding due to unknown interaction between erlotinib and the developing fetus or newborns potentially exposed to erlotinib by ingestion of lactated milk; all females of childbearing potential must have a blood test within 2 weeks prior to randomization to rule out pregnancy * Women of childbearing potential and sexually active males must be strongly advised to use an accepted and effective method of contraception * Patients must not have clinically significant ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, symptomatic or uncontrolled cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Patient must meet the following criteria: * Non-squamous histology * No antecedent hemoptysis * International normalized ratio (INR) =\< 3 within 4 weeks (28 days) prior to randomization * Patients may be on a stable regimen of therapeutic anticoagulation or may be receiving prophylactic anticoagulation of venous access devices, provided that coagulation studies met entry criteria; 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 due to an increased risk of bleeding with bevacizumab * No history of untreated brain metastases NOTE: Recent data (PASSPORT, ATLAS, AIRES) suggest that bevacizumab can be given in patients with treated brain metastases; investigators can use their discretion in deciding whether to use bevacizumab in patients who fulfill these criteria * Urine dipstick must be =\< 0-1+ within 4 weeks (28 days) of randomization. If urine dipstick is \> 1+ then the Urine Protein Creatinine (UPC) ratio must be calculated * Patients must have no history of thrombotic or hemorrhagic disorders * Patients with history of hypertension must be well-controlled (blood pressure \[BP\] =\< 150/90 within 4 weeks \[28 days\] of randomization) and on a stable regimen of anti-hypertensive therapy (within 4 weeks of randomization) * Patients must not have serious non-healing wound ulcer, bone fracture, or major surgical procedure within 28 days prior to randomization * 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 6 months prior to randomization * Patients must not have a history of abdominal fistula, gastrointestinal perforation or intra-abdominal abscess within 6 months prior to randomization * Patients must not have significant vascular disease (e.g., aortic aneurysm, requiring surgical repair or recent peripheral arterial thrombosis) within 6 months prior to randomization * Patients must not have clinically significant cardiovascular disease including: * History of cerebral vascular accident (CVA) within 6 months * New York Heart Association grade II or greater congestive heart failure * Serious and inadequately controlled cardiac arrhythmia * Clinically significant peripheral vascular disease (symptomatic with intermittent claudications or \< 6 months from a bypass operation)