Olaparib, Cediranib Maleate, and Standard Chemotherapy in Treating Patients With Small Cell Lung Cancer

Inclusion Criteria: * Histologically or cytologically confirmed diagnosis of extensive-stage small cell lung cancer with no prior systemic treatment * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as \>= 20 mm (\>= 2 cm) with conventional techniques or as \>= 10 mm (\>= 1 cm) with spiral computed tomography (CT) scan, magnetic resonance imaging (MRI), or calipers by clinical exam * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * White blood cell count (WBC) \>= 3 x 10\^9/L (within 28 days prior to administration of therapy) * No features suggestive of myelodysplastic syndrome (MDS)/acute myeloid leukemia (AML) on peripheral blood smear (within 28 days prior to administration of therapy) * Absolute neutrophil count \>= 1,500/mcL (within 28 days prior to administration of therapy) * Platelets \>= 100,000/mcL (within 28 days prior to administration of therapy) * Hemoglobin \>= 10 g/dL with no blood transfusion within 28 days of initiation of therapy (within 28 days prior to administration of therapy) * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) (within 28 days prior to administration of therapy) * Aspartate aminotransferase (AST) serum glutamic-oxaloacetic transaminase (SGOT)/alanine aminotransferase (ALT) serum glutamate pyruvate transaminase (SGPT) =\< 2.5 x institutional ULN, unless liver metastases are present and then =\< 5 x institutional ULN is acceptable (within 28 days prior to administration of therapy) * Creatinine clearance \>= 50 mL/min (within 28 days prior to administration of therapy) * Proteinuria - urine protein:creatinine ratio (UPC) of =\< 1 OR =\< 2+ proteinuria on two consecutive urinalysis/dipstick tests taken no less than 1 week apart; patients with 2+ proteinuria on dipstick must also have a UPC of =\< 0.5 on 2 consecutive samples (within 28 days prior to administration of therapy) * Ability to swallow and retain oral medication * The effects of olaparib and cediranib on the developing human fetus are unknown; for this reason and because other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential and male patients and their partners who are sexually active must agree to use two highly effective forms of contraception in combination for the duration of study participation and for 3 months after completion of olaparib and cediranib administration; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately * Postmenopausal or evidence of non-pregnant status for women of childbearing potential as confirmed by a negative urine or serum pregnancy test within 7 days prior to the start of therapy; postmenopausal status is defined as: * Age \>= 60 years, or * Age \< 60 with any one or more of the conditions below: * Amenorrheic for \>= 1 year in the absence of chemotherapy and/or hormonal treatments, * Luteinizing hormone and/or follicle stimulating hormone and/or estradiol levels in the post-menopausal range, * Radiation-induced oophorectomy with last menses \> 1 year ago, * Chemotherapy-induced menopause with \> 1 year interval since last menses, * Surgical sterilization (bilateral oophorectomy or hysterectomy) * Ability to understand and the willingness to sign a written informed consent document * Participants must have archival tumor tissue available for analysis (minimum 20 5 um slide) or be able to undergo a baseline fresh tumor tissue biopsy * Adequately controlled blood pressure; (defined as systolic blood pressure \[SBP\] of =\< 140 mmHg and diastolic blood pressure \[DBP\] of =\< 90 mmHg) on maximum of three antihypertensive medications; participants must have a blood pressure (BP) of =\< 140/90 taken in the clinic or hospital setting by a medical professional within 2 weeks prior to starting on study; it is strongly recommended that participants who are on 3 antihypertensive medications be followed by a cardiologist or a primary care physician for management of BP while on study * Adequately controlled thyroid function, with no symptoms of thyroid dysfunction; patients can be on thyroid hormone replacement medication; asymptomatic patients with elevated thyroid stimulating hormone (TSH) with normal T4/T3 are allowed to enroll, and recommended to follow with routine thyroid function test Exclusion Criteria: * Patients who have had major surgery or trauma within 28 days prior to entering the study; patients must have recovered from any effects of any major surgery and surgical wound should have healed prior to starting treatment * Patients who have had radiotherapy within 14 days prior to entering the study * Patients with a non-healing wound, fracture, or ulcer * Patients who have not recovered from adverse events due to prior anti-cancer therapy (i.e., have residual toxicities \> Common Terminology Criteria for Adverse Events \[CTCAE\] grade 1 or baseline, with the exception of alopecia) * Patients who are receiving any other investigational agents * Patients with symptomatic central nervous system (CNS) metastases or leptomeningeal carcinomatosis should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events; exceptions include patients with previously-treated CNS metastases or those with are asymptomatic, subcentimeter metastases, and have no requirement for steroids or anti-seizure medication for at least one week prior to study entry; screening with CNS imaging studies (CT scan or MRI) is required * History of allergic reactions attributed to compounds of similar chemical or biologic composition to olaparib, cediranib, carboplatin, cisplatin, or etoposide * Patients with a history of myelodysplastic syndrome (MDS) * Patients with a history of acute myeloid leukemia (AML), or patients with a history of any other primary malignancy within 3 years prior to initiation of treatment on this study; exceptions include: patients with a history of malignancies (other than AML) that were treated curatively and have not recurred within 3 years prior to study entry; resected basal and squamous cell carcinomas of the skin; and completely resected carcinoma in situ of any type * Patients with clinically significant gastrointestinal abnormalities including, but not limited to: * Clinically significant signs and/or symptoms of bowel obstruction within 3 months prior to starting treatment * History of intra-abdominal abscess within 3 months prior to starting treatment * History of gastrointestinal (GI) perforation within 6 months prior to starting treatment * Evidence of abdominal fistula within 6 months prior to starting treatment; history of abdominal fistula will be considered eligible if the fistula was surgically repaired, and there has been no evidence of fistula for at least 6 months prior to starting treatment, and patient is deemed to be at low risk of recurrent fistula * Patients with a history of cerebrovascular accident including transient ischemic attack (TIA), pulmonary embolism or insufficiently treated deep venous thrombosis (DVT) within the past 3 months; Note: Participants with recent DVT who have been treated with therapeutic anti-coagulants for at least 6 weeks are eligible, with the exception of participants being treated with warfarin, which is prohibited on this study; other oral anti-coagulants may be allowed after discussion with overall principal investigator (PI), but short half-life low molecular weight heparins are strongly preferred * Patients with evidence of active bleeding diathesis * Patients with hemoptysis in excess of 2.5 mL within 6 weeks prior to the first dose of study medication * Patients receiving any medications or substances that are potent inhibitors or inducers of CYP3A4 are ineligible; the required washout period for strong inhibitors is 2 weeks and at least one week for moderate inhibitors; the required washout period prior to starting olaparib is 5 weeks for enzalutamide or phenobarbital and 4 weeks for other agents * Patients requiring concomitant therapy with phenytoin, phenobarbital, carbamazepine, or valproic acid * 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; specifically, patients with any of the following within 6 months prior to starting treatment are excluded: * Acute myocardial infarction * Unstable angina * New York Heart Association functional classification of III or IV * Left ventricular ejection fraction (LVEF) \< lower limit of normal (LLN) per institutional guidelines, or 55% * Prior allogeneic bone marrow transplant or double umbilical cord blood transplantation * Patients with active hepatitis (B or C) * Patients with active pneumonitis * Pregnant women are excluded from this study because olaparib and cediranib are agents with the potential for teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with olaparib or cediranib, breastfeeding should be discontinued if the mother is treated with olaparib or cediranib; these potential risks may also apply to other agents used in this study * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with olaparib and cediranib; in addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy; appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated * Patients must be willing and able to check and record daily blood pressure readings if receiving cediranib