• Any confirmation (cytologic, histologic, or pathologic) of extensive stage small cell lung cancer at any site, either primary or metastases

• Partial response (PR) or stable disease (SD) after 4-6 cycles of etoposide/platinum (E/P) doublet plus atezolizumab by re-staging scans (positron emission tomography \[PET\]/computed tomography \[CT\] scan, diagnostic CT scan, magnetic resonance imaging \[MRI\] optional per treating physician); atezolizumab should continue through randomization. Patients must be randomized within 9 weeks of last dose of etoposide/platinum (if not receiving PCI) or 6 weeks from completion of prophylactic cranial irradiation (PCI)

‣ NOTE: Patients must have at least 3 cycles of E/P plus atezolizumab. They can have one cycle of induction E/P without concurrent atezolizumab if unable to receive concurrent E/P combined with atezolizumab for all cycles of induction therapy

• Patients must have measurable disease (per Response Evaluation Criteria in Solid Tumors \[RECIST\]) and 3 or fewer observable liver metastases and no evidence of progressive disease (per RECIST) at time of enrollment

• At time of enrollment after induction E/P chemotherapy and atezolizumab, if there is a pleural effusion, patients will be eligible if thoracentesis is cytologically negative 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

• Appropriate stage for study entry based on the following diagnostic workup:

‣ History/physical examination within 14 days prior to registration;

⁃ Imaging within 42 days prior to registration to include:

• MRI brain with contrast or CT brain with contrast

∙ CT chest, abdomen and pelvis or whole body PET/CT scan any time after the fourth cycle of chemotherapy and prior to registration

• Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 within 14 days prior to registration

• Absolute neutrophil count (ANC) \>= 1,000/cells/mm\^3 (within 14 days prior to registration)

• Platelets \>= 75,000 cells/mm\^3 (within 14 days prior to registration)

• Hemoglobin \>= 8 g/dL (within 14 days prior to registration)

• Total bilirubin =\< 1.5 x upper limit of normal (ULN) (within 14 days prior to registration)

• Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3.0 x ULN (AST and/or ALT =\< 5 ULN for patients with liver involvement) (within 14 days prior to registration)

• Alkaline phosphatase =\< 2.5 x ULN (=\< 5 ULN for patients with documented liver involvement or bone metastases) (within 14 days prior to registration)

• Adequate renal function = Creatinine clearance \>=40 mL/min by the Cockcroft-Gault (C-G) equation: (within 14 days prior to registration)

• Upfront radiation therapy of symptomatic metastatic site is permissible if causing symptoms such as pain or impending fracture

• Patients with brain metastases are eligible after receiving whole brain radiation before enrollment (anytime during induction systemic therapy). Whole brain radiation can be delivered with hippocampal sparing or 3-D conformal technique. Patients with irradiated brain metastases are eligible if they are clinically stable from a neurological standpoint after completing radiotherapy (e.g. not having uncontrolled seizures) and do not require use of steroids above a dose of 10 mg of prednisone daily

• For women of childbearing potential, a negative serum or urine pregnancy test within 14 days prior to registration.

‣ Note: 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)

• Patients positive for human immunodeficiency virus (HIV) on effective anti-retroviral therapy with undetectable viral load within 6 months and a stable regimen of highly active anti-retroviral (HAART) HIV-positive patients must have no requirement for concurrent antibiotics or antifungal agents for the prevention of opportunistic infections

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