Inclusion Criteria:

          -  Patient must have a histologically confirmed diagnosis of small-cell lung cancer
             (SCLC)

          -  Patient must have an MRI of the brain performed within 28 days prior to registration
             documenting no evidence of brain metastases or leptomeningeal disease. Patient also
             must not have a history of brain metastases or leptomeningeal disease

          -  Immunotherapy concurrent with and/or adjuvant to first-line therapy is allowed at the
             discretion of the treating physician. Patients with limited-stage (LS)-SCLC must have
             completed platinum-based chemotherapy and either definitive thoracic radiotherapy
             (including stereotactic body radiation therapy [SBRT] for early-stage T1-2 N0 M0
             disease who do not undergo surgery) or definitive surgical resection; thoracic
             radiation in addition to definitive surgical resection is allowed at the discretion of
             the treating physician, but is not required. Patients with extensive-stage (ES)-SCLC
             must have completed platinum-based chemotherapy either with or without thoracic
             radiotherapy at the discretion of the treating physician

          -  All adverse events from prior treatment must have resolved to =< grade 2 (Common
             Terminology Criteria for Adverse Events [CTCAE] version 5.0) prior to randomization

          -  Patient must have had a response to first-line therapy and no evidence of progression
             in opinion of the treating investigator. Systemic imaging (computed tomography [CT] or
             positron emission tomography [PET]/CT including the chest and abdomen) must be
             performed within 28 days prior to randomization

          -  No more than 8 weeks may have elapsed between day 1 of the last cycle of chemotherapy
             and randomization

          -  Patient must not have received prior radiotherapy to the brain or whole brain
             radiotherapy. Patients who have undergone prior stereotactic radiosurgery for benign
             tumors or conditions (e.g., acoustic neuroma, grade I meningioma, trigeminal
             neuralgia) may be considered on a case-by-case basis

          -  Patient must have Zubrod performance status of 0-2

          -  Patient must not have a contraindication to MR imaging, such as implanted metal
             devices or foreign bodies

          -  Patient must not have a contraindication to gadolinium contrast administration during
             MR imaging, such as allergy or insufficient renal function

          -  Patient must not have other metastatic malignancies requiring current active treatment

          -  Patient must not have any severe active comorbidities, defined as follows:

               -  Unstable angina and/or congestive heart failure requiring hospitalization within
                  6 months prior to randomization

               -  Transmural myocardial infarction within 6 months prior to randomization

               -  Acute bacterial or fungal infection requiring intravenous antibiotics at the time
                  of randomization

               -  Chronic obstructive pulmonary disease exacerbation or other acute respiratory
                  illness precluding study therapy at the time of randomization

               -  Severe hepatic disease defined as a diagnosis of Child-Pugh class B or C hepatic
                  disease

               -  Human immunodeficiency virus (HIV) positive with CD4 count < 200 cells/microliter

                    -  Note that patients who are HIV positive are eligible, provided they are
                       under treatment with highly active antiretroviral therapy (HAART) and have a
                       CD4 count >= 200 cells/microliter within 16 weeks prior to randomization

                    -  Note also that HIV testing is not required for eligibility for this protocol

          -  Patient must not be pregnant because of fetal risks from radiation exposure. Men must
             have agreed to use an effective contraceptive method during PCI and for six months
             after completing PCI. Women of reproductive potential must have agreed to use an
             effective contraceptive method during PCI. 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 patient chooses to become heterosexually active during the time
             period for use of contraceptive measures outlined in the protocol, he/she is
             responsible for beginning contraceptive measures

          -  Patients who speak and understand English or French must agree to participate in
             cognitive function testing

          -  Patient must be offered the opportunity to have specimens submitted for banking

          -  Patients must be informed of the investigational nature of this study and must sign
             and give written informed consent in accordance with institutional and federal
             guidelines

          -  As a part of the Oncology Patient Enrollment Network (OPEN) randomization process the
             treating institution?s identity is provided in order to ensure that the current
             (within 365 days) date of institutional review board approval for this study has been
             entered in the system