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

The primary objective of this single arm study is to estimate the progression free survival of previously-untreated patients with extensive stage small cell lung cancer. Patients will receive initial chemo-immunotherapy followed by maintenance therapy with durvalumab and oral ceralasertib.

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 \/= 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 \