Inclusion Criteria:
* Provision of signed and dated written informed consent form prior to any mandatory study specific procedures, sampling, and analyses. For inclusion in i) the optional exploratory genetic research and ii) the optional biomarker research, patients must fulfill the following criteria:
* Provision of informed consent for genetic research prior to collection of sample;
* Provision of informed consent for biomarker research prior to collection of sample;
* If a patient declines to participate in the optional exploratory genetic research or the optional biomarker research, there will be no penalty or loss of benefit to the patient. The patient will not be excluded from other aspects of the study
* At least one lesion (measurable and/or non-measurable) that can be accurately assessed at baseline by computed tomography (CT) and is suitable for repeated assessment
* Patients with previously treated brain metastases that are asymptomatic for at least 14 days and only require prednisone equivalent of 10 mg daily or less prior to study treatment
* Histological or cytological documented ES-SCLC: American Joint Committee on Cancer (AJCC) stage IV SCLC (T any, N any, M1 a/b), including patients with T3-4 due to multiple lung nodules that are too extensive or have tumor/nodal volume that is too large to be encompassed in a tolerable radiation plan
* No prior systemic therapy for ES-SCLC, including, but not limited to, chemotherapy, PARP inhibitor, and PD-1/PD-L1 checkpoint inhibitors. Palliative radiation is allowed if completed a minimum of three days prior to beginning of study treatment
* Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 at enrollment
* Body weight \> 30 kg
* Hemoglobin \>=10.0 g/dL with no blood transfusion in the past 28 days (measured within 28 days prior to administration of study treatment)
* Absolute neutrophil count \>= 1.5 x 10\^9 /L (measured within 28 days prior to administration of study treatment)
* Platelet count \>= 100 x 10\^9/L (measured within 28 days prior to administration of study treatment)
* Serum bilirubin =\<1.5 x institutional upper limit of normal (ULN) (measured within 28 days prior to administration of study treatment)
* Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2.5 x institutional ULN, unless liver metastases are present in which case they must be =\< 5 x ULN (measured within 28 days prior to administration of study treatment)
* Calculated estimated creatinine clearance \>= 51 mL/min using the Cockcroft- Gault equation or based on a 24-hour urine test (measured within 28 days prior to administration of study treatment)
* Evidence of post-menopausal status or evidence of non-childbearing status for women of childbearing potential: negative urine or serum pregnancy test within 28 days of study treatment and confirmed prior to treatment on day 1. Postmenopausal status is defined as:
* Amenorrheic for 1 year or more following cessation of exogenous hormonal treatments
* Luteinizing hormone (LH) and follicle stimulating hormone (FSH) levels in the post-menopausal range for women under 50
* 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)
* Women of childbearing potential and their partners, who are sexually active, must agree to the use of TWO highly effective forms of contraception in combination. This should be started from the signing of the informed consent and continue throughout the period of taking study treatment and for at least 3 months after last dose of study drug(s)
* Male patients must use a condom during treatment and for 3 months after the last dose of study treatment when having sexual intercourse with a pregnant woman or with a woman of childbearing potential. Female partners of male patients should also use a highly effective form of contraception if they are of childbearing potential. Male patients should not donate sperm throughout the period of taking study treatment and for 3 months following the last dose of study treatment
* Subject is willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations including follow-up
Exclusion Criteria:
* Histology other than SCLC
* Prior systemic therapy for ES-SCLC (e.g. chemotherapy, PARP inhibitor, other DNA damage response \[DDR\] inhibitors, PD-1/PD-L1 inhibitors)
* Patients with untreated brain metastases
* Patients with spinal cord compression unless considered to have received definitive treatment for this and evidence of clinically stable disease for 28 days
* Major surgical procedure (as defined by the Investigator) within 28 days prior to the first dose of study treatment and patients must have recovered from any effects of any major surgery. Note: Local surgery of isolated lesions for palliative intent is acceptable
* Other malignancy unless curatively treated with no evidence of disease for \>= 3 years except:
* Adequately treated non-melanoma skin cancer.
* Curatively treated in situ cancer of the cervix; ductal carcinoma in situ (DCIS); stage 1, grade 1 endometrial carcinoma; and in situ bladder cancer
* Any concurrent anticancer therapy
* Resting electrocardiogram (ECG) indicating uncontrolled, potentially reversible cardiac conditions, as judged by the investigator (e.g. unstable ischemia, uncontrolled symptomatic arrhythmia, congestive heart failure, QT corrected by Fridericia \[QTcF\] prolongation \> 500 ms, electrolyte disturbances, etc.), or patients with congenital long QT syndrome
* Current or prior use of immunosuppressive medication within 14 days prior to cycle 1 (C1) of study treatment, with the exceptions of intranasal and inhaled corticosteroids, or systemic corticosteroids at physiological doses, which are not to exceed 10 mg/day of prednisone or an equivalent corticosteroid
* Active or prior documented autoimmune disease within the past 2 years. NOTE: vitiligo, alopecia, chronic skin condition that does not require systemic therapy, psoriasis not requiring systemic treatment (within the past 2 years), and hypothyroidism (if stable on hormonal therapy) are not exclusion criteria
* Active or prior documented inflammatory bowel disease (e.g., Crohn's disease, ulcerative colitis) or pneumonitis
* Immunocompromised patients, e.g., patients who are known to be serologically positive for human immunodeficiency virus (HIV)
* Previous allogenic bone marrow transplant or double umbilical cord blood transplantation (dUCBT)
* Patients considered high medical risk due to a serious, uncontrolled medical disorder, non-malignant systemic disease or active, uncontrolled infection. Examples include, but are not limited to, uncontrolled ventricular arrhythmia, recent (within 3 months) myocardial infarction, uncontrolled major seizure disorder, unstable spinal cord compression, superior vena cava syndrome, extensive interstitial bilateral lung disease on high resolution computed tomography (HRCT) scan or any psychiatric disorder that prohibits obtaining informed consent
* Patients with myelodysplastic syndrome (MDS) / acute myeloid leukemia (AML) or with features suggestive of MDS/AML
* Whole blood transfusions in the last 120 days prior to entry to the study (packed red blood cells and platelet transfusions are acceptable outside of 28 days prior to treatment)
* Patients unable to swallow orally administered medication and patients with gastrointestinal disorders likely to interfere with absorption of the study medication
* Concomitant use of known strong CYP3A inhibitors (e.g. itraconazole, telithromycin, clarithromycin, protease inhibitors boosted with ritonavir or cobicistat, indinavir, saquinavir, nelfinavir, boceprevir, telaprevir) or moderate CYP3A inhibitors (e.g. ciprofloxacin, erythromycin, diltiazem, fluconazole, verapamil). The required washout period prior to starting study treatment is 2 weeks
* Concomitant use of known strong (e.g. phenobarbital, enzalutamide, phenytoin, rifampicin, rifabutin, rifapentine, carbamazepine, nevirapine and St John's Wort) or moderate CYP3A inducers (e.g. bosentan, efavirenz, modafinil). The required washout period prior to starting study treatment is 5 weeks for enzalutamide or phenobarbital and 3 weeks for other agents
* Participation in another clinical study with an investigational product (IP) administered in the last 6 months
* Involvement in the planning and/or conduct of the study
* Previous enrollment in the present study
* Receipt of live attenuated vaccination within 30 days prior to study entry
* Female subjects who are pregnant, breast-feeding or male or female patients of reproductive potential who are not employing two highly effective methods of birth control
* Any condition that, in the opinion of the investigator, would interfere with evaluation of study treatment or interpretation of patient safety or study results
* Known allergy or hypersensitivity to durvalumab, olaparib or any excipients
