Pembrolizumab and Olaparib Treatment of Extensive Small Cell Lung Cancer (ES-SCLC)

The Inclusion Criteria: 1. The participant (or legally acceptable representative if applicable) provides written informed consent for the trial. 2. Male/female participants who are at least 18 years of age on the day of signing informed consent. 3. Cytologically/histologically confirmed diagnosis of SCLC per the Veterans Administration Lung Study Group (VALG) staging system will be enrolled in this study. Patients must have extensive stage (ES) SCLC defined as Stage IV (T any, N any, M 1a/b/c) by the American Joint Committee on Cancer, Eighth Edition. 4. Possibility of obtaining tissue sample, via a biopsy of the primary tumour or metastatic tumour tissue, within the 6 weeks prior to study entry. An archival biopsy is acceptable as long as there has been no intervening anticancer treatment since the time the biopsy was obtained to enrolment in this clinical study and as long as it was within 6 weeks of study entry. Tissue sample would consist of formalin-fixed, paraffin-embedded tumour tissue blocks, or, from formalin-fixed paraffin-embedded tumor tissue block, at least five re-cut, unstained sections of 5 μM thickness for immunohistochemical analysis and five unstained sections of 10 μM thickness for NGS, presented on slides or cell-block. 5. No prior systemic treatment for ES-SCLC. Patients who have received prior chemo-radiotherapy for limited-stage SCLC must have been treated with curative intent and experienced a treatment free interval of at least 6 months since the last chemotherapy, radiotherapy, or chemoradiotherapy cycle from diagnosis of ES-SCLC. 6. Patients with thoracic radiotherapy clinically indicated (e.g. mediastinal syndrome) could be enrolled providing they receive radiotherapy not before 15 days since the start of the experimental treatment. Patients who received radiation therapy to the lung fields that is \> 30 Gy within 6 months of the first dose of trial treatment, will be excluded. 7. Presence of target lesions by RECIST 1.1. Lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions. 8. Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1. Evaluation of ECOG is to be performed within 7 days prior to the date of registration . 9. Patients with paraneoplastic syndromes can be enrolled if an autoimmune origin can be excluded. Autoimmune origin will be defined according to local practice. 10. Life expectancy ≥12 weeks. 11. Capacity to swallow. 12. Ability to comply with the study protocol, in the investigator's judgment. 13. Have adequate organ function. Specimens must be collected within 10 days prior to the registration day. 14. Negative human immunodeficiency virus (HIV) test at screening. 15. Negative total hepatitis B core antibody (HBcAb) test at screening, or positive total HBcAb test followed by a negative hepatitis B virus (HBV) DNA test at screening. The HBV DNA test will be performed only for patients who have a positive total HBcAb test. 16. Negative hepatitis C virus (HCV) antibody test at screening, or positive HCV antibody test followed by a negative HCV RNA test at screening. The HCV RNA test will be performed only for patients who have a positive HCV antibody test. 17. Male participants: Male patients must use a condom during treatment and for 3 months after the last dose of olaparib 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. 18. Female participants: A female participant is eligible to participate if she is not pregnant, not breastfeeding, and at least one of the following conditions applies: 1. Not a woman of childbearing potential (WOCBP) as defined in Appendix F, or 2. A WOCBP who agrees to follow the contraceptive guidance in Appendix F during the treatment period and for at least 120 days after the last dose of study treatment. Exclusion Criteria: 1. Known active central nervous system (CNS) metastases and/or carcinomatous meningitis. Participants with previously treated brain metastases may participate provided they are radiologically stable, i.e. without evidence of progression for at least 4 weeks by repeat imaging (note that the repeat imaging should be performed during study screening), clinically stable and without requirement of steroid treatment for at least 14 days prior to first dose of study intervention. 2. Active or history of autoimmune disease or immune deficiency which has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs), including, but not limited to, myasthenia gravis, myositis, autoimmune hepatitis, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, antiphospholipid antibody syndrome, Wegener granulomatosis, Sjögren syndrome, Guillain-Barré syndrome, or multiple sclerosis, with the following exceptions: * Patients with a history of autoimmune-related hypothyroidism who are on thyroid replacement hormone are eligible for the study. * Patients with controlled Type 1 diabetes mellitus who are on an insulin regimen are eligible for the study. * Patients with eczema, psoriasis, lichen simplex chronicus, or vitiligo with dermatologic manifestations only (e.g., patients with psoriatic arthritis are excluded) are eligible for the study provided all of following conditions are met: * Rash must cover less than 10% of body surface area; * Disease is well controlled at baseline and requires only low-potency topical corticosteroids; * No occurrence of acute exacerbations of the underlying condition requiring psoralen plus ultraviolet A radiation, methotrexate, retinoids, biologic agents, oral calcineurin inhibitors, or high-potency or oral corticosteroids within the previous 12 months; * Replacement therapy (eg., thyroxine, insulin, or physiologic