Chemo-Immunotherapy Followed by Durvalumab and Ceralasertib in Treatment Naïve Patients With Extensive Stage Small Cell Lung Cancer

Inclusion Criteria: * Written informed consent and HIPAA authorization for release of personal health information. NOTE: HIPAA authorization may be included in the informed consent or obtained separately. * Age \>= 18 years at the time of consent. * ECOG Performance Status of 0-1 within 14 days prior to registration (Appendix A of Protocol). * Histological or cytological confirmed small cell lung carcinoma * Extensive stage disease * Patient must be considered suitable to receive a platinum-based chemotherapy as 1st line treatment for ES-SCLC. Chemotherapy must contain either Carboplatin or Cisplatin in combination with Etoposide. * Measurable disease according to RECIST v1.1 for solid tumors within 28 days prior to registration. * Prior treatment must be completed within the following number of days prior to registration: --Palliative radiation: for painful bony lesion must be completed prior to registration and recovered from significant bone marrow toxicity. For patients who received WBRT, 14 days washout is required prior to study therapy. Patient's must be off steroids without worsening of symptoms related to brain metastases. Patient should be on stable doses of anti-convulsant. * Demonstrate adequate organ function as defined in the protocol; all screening labs to be obtained within 14 days prior to registration * Hematological * Absolute Neutrophil Count (ANC) \>/= 1500/mm\^3 * Platelet \>/= 100,000/mm\^3 * Hemoglobin (Hgb) \>/= 9 g/dL * Renal * Creatinine \</= 1.5 x ULN * Calculated creatinine clearance \>/= 50 mL/min using the Cockcroft-Gault formula if creatinine is more than 1.5 x ULN (60 mL/min if receiving Cisplatin) * Hepatic * Bilirubin \</= 1.5 x upper limit of normal (ULN), \</= 3 x ULN if history of Gilbert Syndrome * Aspartate aminotransferase (AST) \</= 2.5 x ULN (if liver metastases then \</= 5 x ULN) * Alanine aminotransferase (ALT) \</= 2.5 x ULN (if liver metastases then \</= 5 x ULN) * Female subjects of childbearing potential and non-sterilized male subjects who intend to be sexually active during the study must agree to use a highly effective method of contraception from the time of screening, throughout the total duration of the drug treatment, and for 6 months after the last dose of study drug treatment. * Evidence of post-menopausal status or negative urinary or serum pregnancy test for female pre-menopausal patients. Women will be considered post-menopausal if they have been amenorrheic for 12 months without an alternative medical cause. The following age-specific requirements apply: * Women \<50 years of age would be considered post-menopausal if they have been amenorrheic for 12 months or more following cessation of exogenous hormonal treatments and if they have luteinizing hormone and follicle-stimulating hormone levels in the post-menopausal range for the institution or underwent surgical sterilization (bilateral oophorectomy or hysterectomy). * Women ≥50 years of age would be considered post-menopausal if they have been amenorrheic for 12 months or more following cessation of all exogenous hormonal treatments, had radiation-induced menopause with last menses \>1 year ago, had chemotherapy-induced menopause with last menses \>1 year ago, or underwent surgical sterilization (bilateral oophorectomy, bilateral salpingectomy or hysterectomy). * As determined by the enrolling physician or protocol designee, ability of the subject to understand and comply with study procedures for the entire length of the study * Ability to swallow and retain oral medication * Must have a life expectancy of at least 12 weeks Exclusion Criteria: * Prior systemic therapy for extensive stage or recurrent SCLC * Patients with recurrent SCLC, who received chemotherapy or definitive chest radiation in the past for limited-stage SCLC. * Clinically significant active infection requiring systemic therapy * Pregnant or breastfeeding (NOTE: breast milk cannot be stored for future use while the mother is being treated on study). * Participants who have undergone major surgery within 28 days before first dose of study drug * Participants who are currently receiving any other investigational agents * Active malignancy requiring therapy other than small cell lung cancer, excluding: non-melanoma skin cancer, noninvasive colonic polyps, superficial bladder tumors, cervical cancer in-situ, ductal carcinoma in situ of the breast, monoclonal B-cell lymphocytosis, or monoclonal gammopathy of undetermined significance. * Diagnosis of immunodeficiency or is receiving systemic steroid therapy (\> 10 mg of prednisone or equivalent) or any other form of immunosuppressive therapy within 7 days prior to study enrolment. Patient's on physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. Topical, inhaled or intra-articular steroids are not considered as systemic steroids. Steroids as premedication for hypersensitivity reaction (e.g. CT scan premedication) or prior to chemotherapy is allowed. * Active autoimmune or inflammatory disorders (including inflammatory bowel disease \[e.g., colitis or Crohn's disease\], systemic lupus erythematosus, or Wegener syndrome \[granulomatosis with polyangiitis, Graves' disease, rheumatoid arthritis, hypophysitis, uveitis, etc\]). The following are exceptions to this criterion: * Patients with vitiligo or alopecia * Patients with hyperthyroidism or hypothyroidism (e.g., following Hashimoto syndrome) clinically stable on hormone replacement * Any chronic skin condition that does not require systemic immunosuppressive therapy * Patients with celiac disease controlled by diet alone * Diabetes mellitus with or without insulin replacement therapy * Has history of immune therapy related pneumonitis that required steroids * Patients with untreated or symptomatic central nervous system (CNS) metastases or leptomeningeal carcinomatosis will be excluded. Previously treated CNS metastases and have no requirement for steroids for at least 2 weeks prior to study entry is allowed. Anticonvulsant therapy at a stable dose is permitted and must not have seizures for at least 2 weeks prior to study entry. May have residual symptoms as new baseline. Brain imaging with either MRI (preferred) or CT with contrast must be performed on all subjects at screening to evaluate brain metastases. * Known history of Hepatitis B (known positive HBV surface antigen (HBsAg) result), hepatitis C, or human immunodeficiency virus (positive HIV 1/2 antibodies). Patients positive for hepatitis C (HCV) antibody are eligible only if polymerase chain reaction is negative for HCV RNA * Known history of active tuberculosis * History of allogeneic stem cell or solid organ transplant * History of Ataxia telangiectasia * Uncontrolled intercurrent illness including, but not limited to, serious and active uncontrolled infection, symptomatic congestive heart failure (NYHA class III-IV), active inflammatory bowel disease, unstable angina pectoris, uncontrolled seizures, or psychiatric illness/social situations that would limit compliance with study requirements * Participants with a known hypersensitivity to durvalumab, ceralasertib or any excipient of the product * Patients who have been vaccinated with live, attenuated vaccines within 4 weeks of first dose of study drug * Refractory nausea and vomiting, chronic gastrointestinal diseases or previous significant bowel resection, with clinically significant sequelae that would preclude adequate absorption of ceralasertib. * Patients weighing \<= 30 Kg. * Participants may not be receiving any medications or substances that are potent inhibitors or inducers of CYP3A4 (Appendix B of the protocol). * There is a required wash-out period of 5 half-lives from such agents prior to starting ceralasertib, or three weeks for St. John's Wort. * For non-potent inhibitors or inducers of CYP3A4, the decision to allow a patient to enroll on the study is per investigator best judgement. Note these include common azole antifungals, macrolide antibiotics, and other medications listed in the concomitant medications section. As part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product. * Exposure of other drugs metabolized by CYP3A4 and/or CYP2B6 may be reduced and additional monitoring may be required. * The use of herbal supplements or 'folk remedies' (and medications and foods that significantly modulate CYP3A activity) should be discouraged. If deemed necessary, such products may be administered with caution and the reason for use documented in the CRF.