Testing the Addition of an Immunotherapy Drug, Atezolizumab, to the Usual Chemotherapy Treatment During Radiation Therapy for Superior Sulcus Non-small Cell Lung Cancer

Inclusion Criteria: * STEP 1 RANDOMIZATION: Participants must have histologically confirmed cT3/T4, N0/1, M0 non-small cell lung cancer (NSCLC) of the superior sulcus arising in the apex of the lung, involving apical chest wall structures (parietal pleura and beyond) above the level of the second rib * STEP 1 RANDOMIZATION: Participants must have eligibility affirmed by a thoracic surgeon, medical oncologist and radiation oncologist. Participant must be a candidate for surgical resection and chemoradiation therapy. The site treating investigator must sign off to indicate that eligibility has been affirmed by each specialist * STEP 1 RANDOMIZATION: Participants may have measurable or non-measurable disease. Measurable disease must be assessed within 28 days prior to Step 1 Randomization. Non-measurable disease must be assessed within 42 days prior to Step 1 Randomization. All known sites of disease must be assessed and documented on the Baseline Tumor Assessment Form * STEP 1 RANDOMIZATION: Participants must have an MRI or CT scan of the brain (with contrast highly recommend) within 42 days prior to Step 1 Randomization * STEP 1 RANDOMIZATION: Participants must have a CT (chest with contrast highly recommended), contrast MRI (thoracic inlet), and FDG-PET/CT performed within 28 days prior to Step 1 Randomization * Note: DWI (Diffusion weighting imaging) is highly recommended on the MRI * STEP 1 RANDOMIZATION: Participants may participate in concomitant non-therapeutic trials (e.g., palliative care assessment or quality of life studies) * STEP 1 RANDOMIZATION: History and physical exam must be obtained within 28 days of Step 1 Randomization * STEP 1 RANDOMIZATION: Participants must have Zubrod performance status of 0-1 documented within 28 days prior to Step 1 Randomization * STEP 1 RANDOMIZATION: Participants must be \>= 18 years old * STEP 1 RANDOMIZATION: Leukocytes \>= 3,000/uL (within 28 days prior to Step 1 Randomization) * STEP 1 RANDOMIZATION: Absolute neutrophil count \>= 1,500/uL (within 28 days prior to Step 1 Randomization) * STEP 1 RANDOMIZATION: Platelets \>= 100,000/uL (within 28 days prior to Step 1 Randomization) * STEP 1 RANDOMIZATION: Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) (within 28 days prior to Step 1 Randomization) * STEP 1 RANDOMIZATION: Participants with known Gilbert disease: total bilirubin =\< 3 x (ULN) (within 28 days prior to Step 1 Randomization) * STEP 1 RANDOMIZATION: Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 3 x institutional ULN (within 28 days prior to Step 1 Randomization) * STEP 1 RANDOMIZATION: Hemoglobin \>= 9 g/dL (within 28 days prior to Step 1 Randomization) * STEP 1 RANDOMIZATION: Participants must not have higher than grade 2 hypercalcemia prior to Step I Randomization * STEP 1 RANDOMIZATION: Participants must have a serum creatinine =\< the institutional upper limit of normal (IULN) OR measured OR calculated creatinine clearance \>= 50 mL/min using the following Cockcroft-Gault formula. This specimen must have been drawn and processed within 28 days prior to Step 1 Randomization * STEP 1 RANDOMIZATION: Participants with known human immunodeficiency virus (HIV)-infection must be receiving anti-retroviral therapy and have undetectable viral load test within 6 months prior to Step 1 Randomization * STEP 1 RANDOMIZATION: Participants with evidence of chronic hepatitis B virus (HBV) infection must have undetectable HBV viral load on suppressive therapy within 28 days prior to Step 1 Randomization * STEP 1 RANDOMIZATION: Participants with a history of hepatitis C virus (HCV) infection must have been treated and cured. Participants with HCV infection who are currently on treatment must have an undetectable HCV viral load within in 28 days prior to Step 1 Randomization * STEP 1 RANDOMIZATION: Participants of reproductive potential must have a negative serum pregnancy test within 14 days prior to Step 1 Randomization * STEP 1 RANDOMIZATION: Participants must be offered the opportunity to participate in specimen banking * STEP 1 RANDOMIZATION: Participants must be informed of the investigational nature of this study and must sign and give informed consent in accordance with institutional and federal guidelines. For participants with impaired decision-making capabilities, legally authorized representatives may sign and give informed consent on behalf of study participants in accordance with applicable federal, local, and Central Institutional Review Board (CIRB) regulations * STEP 2 SURGERY: Participants must have a CT scan of the chest with contrast, FDG-PET/CT scan and MRI scan of the thoracic inlet (with intravenous contrast and DWI highly recommended) within 28 days prior to Step 2 Registration * STEP 2 SURGERY: Participants must be evaluated for appropriateness of surgery by a thoracic surgeon within 6 weeks after completion of neoadjuvant therapy prior to Step 2 Registration * STEP 2 SURGERY: Participant's surgery must occur between 21 and 90 days following the end of participant's final cycle of chemotherapy +/- atezolizumab * STEP 2 SURGERY: Participants must have received at least two cycles of all assigned protocol drugs during neoadjuvant protocol treatment and must have received at least 45 GY RT of the planned 61.2 GY RT during neoadjuvant protocol treatment * STEP 2 SURGERY: Participants must have a Zubrod Performance Status of 0-1 documented within 28 days prior to Step 2 Registration * STEP 2 SURGERY: Participants must have postoperative predicted forced expiratory volume in 1 second (FEV1) \> 35% and postoperative predicted diffusion capacity of the lung for carbon monoxide (DLCO) \> 35%. Pulmonary function tests to ascertain these values must be obtained within 28 days prior to Step 2 Registration * STEP 3 MAINTENANCE THERAPY (ARM 1 ONLY): Participants must have received surgical resection of the lung cancer and side effects must have recovered to =\< grade 2 within 42 days after surgery and prior to Step 3 Registration * STEP 3 MAINTENANCE THERAPY (ARM 1 ONLY): Participants must have a Zubrod Performance Status of 0-1 documented within 28 days prior to Step 3 Registration * STEP 3 MAINTENANCE THERAPY (ARM 1 ONLY): Leukocytes \>= 3,000/uL (within 28 days prior to Step 3 Registration) * STEP 3 MAINTENANCE THERAPY (ARM 1 ONLY): Absolute neutrophil count \>= 1,000/uL (within 28 days prior to Step 3 Registration) * STEP 3 MAINTENANCE THERAPY (ARM 1 ONLY): Platelets \>= 100,000/uL (within 28 days prior to Step 3 Registration) * STEP 3 MAINTENANCE THERAPY (ARM 1 ONLY): Hemoglobin \>= 9 g/dL (within 28 days prior to Step 3 Registration) * STEP 3 MAINTENANCE THERAPY (ARM 1 ONLY): Total bilirubin =\< institutional upper limit of normal (ULN) (within 28 days prior to Step 3 Registration) * STEP 3 MAINTENANCE THERAPY (ARM 1 ONLY): AST and ALT =\< 3 x institutional ULN (within 28 days prior to Step 3 Registration) * STEP 3 MAINTENANCE THERAPY (ARM 1 ONLY): Participants must have adequate kidney function defined as creatinine =\< 1.5 x ULN documented within 28 days prior to Step 3 Registration Exclusion Criteria: * STEP 1 RANDOMIZATION: Participants must not have had prior therapy for this cancer including surgery, chemotherapy, immunotherapy, targeted therapy agent, and/or radiation therapy * STEP 1 RANDOMIZATION: Participants must not have undergone prior radiation to overlapping regions of planned protocol radiation therapy (RT) treatment area * STEP 1 RANDOMIZATION: Participants must not have had prior treatment with CD137 agonists or immune checkpoint blockade therapies, including anti-CTLA-4, anti-PD-1, and anti-PD-L1 therapeutic antibodies * STEP 1 RANDOMIZATION: Participants must not have had prior treatment with systemic immunostimulatory agents (including, but not limited to, interferon and interleukin 2 \[IL-2\]) within 4 weeks prior to Step 1 Randomization * STEP 1 RANDOMIZATION: Participants must not have a known allergy or hypersensitivity to any component of the carboplatin, pemetrexed, cisplatin, etoposide and paclitaxel formulation * STEP 1 RANDOMIZATION: Participants must not have any grade III/IV cardiac disease as defined by the New York Heart Association Criteria (i.e., participants with cardiac disease resulting in marked limitation of physical activity or resulting in inability to carry on any physical activity without discomfort), unstable angina pectoris, and myocardial infarction within 3 months, or serious uncontrolled cardiac arrhythmia * STEP 1 RANDOMIZATION: Participants must not have known active tuberculosis (TB) * STEP 1 RANDOMIZATION: Participants must not have uncontrolled non-malignant pleural effusion, pericardial effusion, or ascites requiring recurrent drainage procedures (more than once a month). Note: Participants with indwelling catheters (e.g., PleurX \[registered trademark\]) are allowed * STEP 1 RANDOMIZATION: Patients must not have undergone prior allogeneic stem cell transplantation or prior solid organ transplantation * STEP 1 RANDOMIZATION: Participants must NOT have a history of severe allergic, anaphylactic, or other known hypersensitivity reactions to chimeric or humanized antibodies or fusion proteins * STEP 1 RANDOMIZATION: Participants must NOT have a known hypersensitivity or allergy to biopharmaceuticals produced in Chinese hamster ovary cells or any component of the atezolizumab formulation * STEP 1 RANDOMIZATION: Participants must not have severe or active infections within 28 days prior to Step 1 Randomization, including but not limited to hospitalization for complications of infection, bacteremia, or severe pneumonia * STEP 1 RANDOMIZATION: Participants must not have active autoimmune disease requiring therapy within the past 6 months. Participants must not have active autoimmune disease that has required systemic treatment within the past two years (i.e., with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. Autoimmune diseases include, but are not limited to, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, vascular thrombosis associated with antiphospholipid syndrome, Wegener's granulomatosis, Sjogren's syndrome, Bell's palsy, Guillain-Barre syndrome, multiple sclerosis, autoimmune thyroid disease, vasculitis, or glomerulonephritis. This protocol includes an immunotherapy agent which can precipitate known autoimmune diseases * STEP 1 RANDOMIZATION: Participants must not have history of idiopathic pulmonary fibrosis, pneumonitis (including drug induced), organizing pneumonia (e.g., bronchiolitis obliterans, cryptogenic organizing pneumonia, etc.), or evidence of active pneumonitis. This protocol includes an immunotherapy agent which can precipitate known pneumonitis * STEP 1 RANDOMIZATION: Participants must not have a prior or concurrent malignancy whose natural history or treatment (in the opinion of the treating physician) has the potential to interfere with the safety or efficacy assessment of the investigational regimen * STEP 1 RANDOMIZATION: Participants must not have received a live attenuated vaccination within 28 days prior to Step 1 Randomization. All coronavirus disease 2019 (COVID-19) vaccines that have received Food and Drug Administration (FDA) approval or FDA emergency use authorization are acceptable * STEP 1 RANDOMIZATION: Participants must not have had a major surgery within 14 days prior to Step 1 Randomization. Participants must have fully recovered from the effects of prior surgery in the opinion of the treating investigator * STEP 1 RANDOMIZATION: Participants must not be pregnant or nursing due to carcinogenic and teratogenic effects of treatment. Women/men of reproductive potential must have agreed to use an effective contraceptive method while on study treatment and for 5 months after the last dose. A woman is considered to be of "reproductive potential" if she has had menses at any time in the preceding 12 consecutive months. In addition to routine contraceptive methods, "effective contraception" also includes heterosexual celibacy and surgery intended to prevent pregnancy (or with a side-effect of pregnancy prevention) defined as a hysterectomy, bilateral oophorectomy or bilateral tubal ligation. However, if at any point a previously celibate participant chooses to become heterosexually active during the time period for use of contraceptive measures outlined, he/she is responsible for beginning contraceptive measures