Inclusion Criteria:

          -  PRIOR TO STEP 1 REGISTRATION

          -  Histologic proof or unequivocal cytologic proof (fine needle aspiration, biopsy or two
             positive sputa) of SCLC within 250 days prior to Step 1 registration

               -  High-grade neuroendocrine carcinoma or combined SCLC and NSCLC is permitted.

          -  Patients must have received chemotherapy and be registered to Step 1 registration no
             earlier than 7 days and no later than 56 days after completing chemotherapy. Note:

               -  Post-chemotherapy restaging imaging must be completed no more than 56 days prior
                  to Step 1 registration.

               -  For patients with extensive-stage small cell lung cancer who are being considered
                  for consolidative thoracic radiotherapy after chemotherapy, concomitant
                  administration of consolidative thoracic radiotherapy and protocol-specified
                  prophylactic cranial irradiation with or without hippocampal avoidance is
                  permitted.

          -  Patients must have a gadolinium contrast-enhanced three-dimensional (3D), spoiled
             gradient (SPGR), magnetization-prepared rapid gradient echo (MP-RAGE), or turbo field
             echo (TFE) MRI scan (see section 11.3 regarding axial T2/FLAIR sequence). To yield
             acceptable image quality, the gadolinium contrast-enhanced three-dimensional SPGR,
             MP-RAGE or TFE axial MRI scan must use the smallest possible axial slice thickness not
             exceeding 1.5 mm. Sites may contact the Imaging Co-Chairs for further information or
             assistance if needed.

               -  This MRI must be obtained within 56 days prior to Step 1 registration. Note: The
                  MRI study is mandatory irrespective of randomization to the experimental or
                  control arm of this study.

          -  Prior to chemotherapy +/- thoracic radiotherapy, patients must be defined as
             limited-stage or extensive-stage SCLC after clinical staging evaluation involving the
             following:

               1. History/physical examination;

               2. CT of the chest and abdomen with contrast (does not have to be done if the
                  patient has had a PET/CT scan prior to initiating chemotherapy or thoracic
                  radiotherapy);

               3. MRI of the brain with contrast or diagnostic head CT with contrast;

               4. For patients without evidence of extensive-stage SCLC on chest and abdomen CT and
                  brain MRI or head CT, a PET/CT or bone scan is required to confirm limited-stage
                  SCLC.

          -  After chemotherapy, patients must be restaged prior to Step 1 registration using the
             same diagnostic work-up as required pre-chemotherapy. Repeat PET/CT or bone scan is
             not required. Patients must have:

               -  History/physical examination within 30 days of Step 1 registration;

               -  No CNS metastases (Repeat MRI required; see Section 3.2.3 for details) within 56
                  days prior to Step 1 registration;

               -  No progression in any site;

               -  Radiographic partial or complete response to chemotherapy in at least one disease
                  site within 56 days prior to Step 1 registration.

                    1. If PET/CT was obtained prior to chemotherapy, either a repeat PET/CT or CT
                       of the chest and abdomen with contrast can be obtained for response
                       assessment.

                    2. Patients who underwent resection for limited-stage SCLC prior to
                       chemotherapy and have no radiographically evident disease for response
                       assessment remain eligible if post-chemotherapy imaging demonstrates no
                       progression.

          -  Zubrod performance status 0-2

          -  Women of childbearing potential and male participants must practice adequate
             contraception

          -  Women of childbearing potential must have a negative qualitative serum pregnancy test
             =< 2 weeks prior to study entry

          -  Patients who are primary English or French speakers are eligible

          -  Patients must sign a study-specific informed consent prior to study entry

          -  PRIOR TO STEP 2 REGISTRATION

          -  The following baseline neurocognitive assessments must be completed and uploaded
             within 10 calendar days after or at the time of Step 1 registration: HVLT-R (recall,
             delayed recall, and recognition), TMT (Parts A and B), and COWA. The neurocognitive
             assessments will be uploaded into the NRG Oncology RAVE System for evaluation by Dr.
             Wefel. Once the upload is complete, within 3 business days, a notification email will
             be sent to the site to proceed to Step 2 registration. At minimum, the HVLT-R delayed
             recall must be able to be scored (i.e. completed without error) in order to be
             eligible.

          -  Patients must have a baseline raw score greater than 2 on the HVLT-R delayed recall

        Exclusion Criteria:

          -  Prior radiotherapy to the head or neck (except for T1 glottic cancer), resulting in
             overlap of radiation fields

          -  Radiographic evidence of CNS metastases

          -  Radiographic evidence of hydrocephalus or other architectural distortion of the
             ventricular system, including placement of external ventricular drain or
             ventriculoperitoneal shunt

          -  Planned concurrent chemotherapy or anti-tumor agent during PCI

               -  Concurrent atezolizumab permitted

          -  Concomitant invasive malignancy or invasive malignancy within the past five years
             other than non-melanomatous skin cancer; history of in situ carcinoma (e.g. ductal
             carcinoma in situ of breast, in situ carcinoma of the cervix, vulva or larynx) is
             permitted

          -  Contraindication to MR imaging, such as implanted metal devices or foreign bodies or
             severe claustrophobia

          -  Severe, active comorbidity, defined as follows:

               -  Unstable angina and/or congestive heart failure requiring hospitalization within
                  the last 6 months

               -  Transmural myocardial infarction within the last 6 months

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

               -  Hepatic insufficiency resulting in clinical jaundice and/or coagulation defects

               -  Chronic obstructive pulmonary disease exacerbation or other respiratory illness
                  requiring hospitalization or precluding study therapy at the time of registration

               -  Uncontrolled, clinically significant cardiac arrhythmias

               -  HIV positive with CD4 count < 200 cells/microliter;

                    1. Note: 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 30 days prior to Step 1 registration.

                    2. Note: HIV testing is not required for eligibility for this protocol.

          -  Pregnant or lactating women or women of childbearing potential and male participants
             who are sexually active and not willing/able to use medically acceptable forms of
             contraception