Inclusion Criteria:

          -  Pathologically (histologically or cytologically) proven diagnosis of limited stage
             small cell lung cancer (Stage Tx, T1-T4, N0-3, M0, American Joint Committee on Cancer
             [AJCC] staging, 8th edition [Ed.]), within 60 days prior to registration

          -  Patients must have received one cycle of platinum/etoposide chemotherapy
             pre-registration (prior to study entry). Study registration must be within 21 days
             from day 1 of the pre-registration cycle of chemotherapy.

          -  Patients must have had measurable disease (per Response Evaluation Criteria in Solid
             Tumors [RECIST], version 1.1) prior to the required cycle of platinum/etoposide
             chemotherapy

          -  Minimal staging requirements include:

               -  History/physical examination within 30 days prior to registration

               -  Positron emission tomography (PET)/computed tomography (CT) scan for staging
                  within 60 days prior to registration

               -  CT chest/abdomen with IV contrast (unless contraindicated based on kidney
                  function) within 60 days prior to registration;

                    -  Note: If contrast allergy exists, premedication per institutional guidelines
                       should be performed prior to obtaining CT with contrast. The only exception
                       to this is a documented life-threatening allergy

               -  Magnetic resonance imaging (MRI) scan of the brain with contrast (preferred) or
                  CT scan of the brain with contrast (allowable if there is a contraindication with
                  MRI with contrast) within 30 days prior to registration

          -  Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 within 30 days
             prior to registration

          -  Absolute neutrophil count (ANC) >= 1, 500/cells/mm^3 (prior to pre-registration cycle)

          -  Platelet count >= 100,000 cells/mm^3 (prior to pre-registration cycle)

          -  Hemoglobin >= 9 g/dL (prior to pre-registration cycle)

          -  Total bilirubin =< 1.5 x upper limit of normal (ULN) (prior to pre-registration cycle)

          -  Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT]) and
             alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 2.0 x
             ULN (prior to pre-registration cycle)

          -  Glomerular filtration rate (GFR) >= 30 mL/min/1.73 m^2 (within 30 days prior to
             registration)

          -  Patients presenting with a pleural effusion will be eligible if thoracentesis is
             cytologically negative and non-bloody or if pleural fluid is too small a volume to
             effectively sample by thoracentesis and does not show increased metabolic activity on
             CT/PET imaging

          -  Negative serum pregnancy test within 14 days of registration for pre-menopausal women
             of childbearing potential

          -  The patient or a legally authorized representative must provide study-specific
             informed consent prior to study entry

          -  Hepatitis B/C testing prior to enrollment for patients that have not been tested
             before. Note: This is required even if the patient has never shown or had symptoms of
             hepatitis

          -  Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral
             therapy with undetectable viral load within 6 months are eligible for this trial

        Exclusion Criteria:

          -  Definitive clinical or radiologic evidence of metastatic disease

          -  Definitive surgical resection of small cell lung cancer

          -  Prior invasive malignancy (except non-melanomatous skin cancer, localized prostate
             cancer, or any early stage cancer treated with curative intent resection) unless
             disease free for a minimum of 2 years (carcinoma in situ of the breast, oral cavity,
             or cervix are all permissible)

          -  More than 1 cycle of prior platinum-based chemotherapy for SCLC prior to enrollment;
             note that prior chemotherapy for a different cancer is allowable

          -  Any prior atezolizumab or other immunotherapy agent

          -  Prior radiotherapy to the lungs or mediastinum that would result in clinically
             significant overlap of radiation therapy fields; prior tangent fields for breast
             cancer with minimal overlap with target volumes are allowed per approval of study
             principal investigators (PIs)

          -  Patients with cytologically positive pleural or pericardial fluid are not eligible

          -  An active, known or suspected autoimmune disease. Patients are permitted to enroll if
             they have vitiligo, type I diabetes mellitus, residual hypothyroidism due to
             autoimmune condition only requiring hormone replacement, psoriasis not requiring
             systemic treatment, or conditions not expected to recur in the absence of an external
             trigger

          -  Active or prior documented inflammatory bowel disease (e.g., Crohn's disease,
             ulcerative colitis)

          -  History of allogeneic organ transplant

          -  History of primary immunodeficiency

          -  Severe, active co-morbidity defined as follows:

               -  Known clinically significant liver disease, including active viral, alcoholic, or
                  other hepatitis, cirrhosis, fatty liver, and inherited liver disease

               -  Any other diseases, metabolic dysfunction, physical examination finding, or
                  clinical laboratory finding giving reasonable suspicion of a disease or condition
                  that contraindicates the use of an investigational drug or that may affect the
                  interpretation of the results or render the patient at high risk from treatment
                  complications

               -  Active tuberculosis

               -  Active hepatitis B (chronic or acute) or hepatitis C infection. Note that if
                  hepatitis status is unknown, hepatitis B/C testing is required

                    -  Patients with past or resolved hepatitis B infection (defined as having a
                       negative hepatitis B surface antigen [HBsAg]) test, a positive anti-HBc
                       (antibody to hepatitis B core antigen), and a negative viral
                       deoxyribonucleic acid (DNA) test (only obtained if HBsAg is found positive)
                       are eligible

                    -  Patients positive for hepatitis C virus (HCV) antibody are eligible only if
                       polymerase chain reaction (PCR) is negative for HCV ribonucleic acid (RNA).
                       (The HCV RNA test must be performed for patients who have a positive HCV
                       antibody test.)

               -  Known immunosuppressive disease, for example history of bone marrow transplant or
                  chronic lymphocytic leukemia (CLL)

               -  Chronic obstructive pulmonary disease (COPD) requiring chronic oral steroid
                  therapy of > 10 mg prednisone daily or equivalent at the time of registration.
                  Inhaled corticosteroids are not exclusionary

               -  Unstable angina and/or congestive heart failure requiring hospitalization within
                  the last 3 months

               -  Transmural myocardial infarction within the last 3 months

               -  Clinically significant interstitial lung disease

          -  A condition requiring systemic treatment with either corticosteroids (> 10 mg daily
             prednisone equivalents) or other immunosuppressive medications within 14 days of study
             drug administration. Inhaled or topical steroids and adrenal replacement doses > 10 mg
             daily prednisone equivalents are permitted in the absence of active autoimmune disease

          -  Pregnancy or women of childbearing potential and men who are sexually active and not
             willing/able to use medically acceptable forms of contraception for the duration of
             study treatment and for 180 days after the last dose of study drug (Arm 2); this
             exclusion is necessary because the treatment involved in this study may be
             significantly teratogenic