Testing the Addition of a New Immunotherapy Drug, Atezolizumab (MPDL3280A), to the Usual Chemoradiation (CRT) Therapy Treatment for Limited Stage Small Cell Lung Cancer (LS-SCLC)

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 pre-registration 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 and CT abdomen with IV contrast (unless contraindicated based on kidney function) within 60 days prior to registration; magnetic resonance imaging (MRI) abdomen with IV contrast allowed in place of CT abdomen * 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 * 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 * Age \>= 18 * 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) * Adequate renal function within 30 days prior to registration defined as follows: Creatinine clearance \>= 30 mL/min by the Cockcroft-Gault (C-G) equation * 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 150 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.