Testing the Use of Targeted Treatment for RET Positive Advanced Non-small Cell Lung Cancer

Inclusion Criteria:

* Participants must have stage IV or recurrent disease
* Participants must have been assigned to S1900F based on biomarker analysis of tissue and/or blood and determined to have RET fusion-positive NSCLC as defined here:

  * Participants must have RET fusion-positive NSCLC as determined by the Foundation Medicine (FMI) tissue-assay or other tumor-based assays such as next generation sequencing (NGS), polymerase chain reaction (PCR), or fluorescent in situ hybridization (FISH), or by cfDNA blood assay as outlined in the LUNGMAP Screening Protocol. Participants previously tested for and determined to have RET-fusion-positive NSCLC outside of LUNGMAP, must also submit tissue for central FMI testing on the LUNGMAP Screening Protocol. Participants with RET fusions detected by IHC alone are not eligible. The testing must be done within a laboratory with Clinical Laboratory Improvement Act (CLIA), International Organization for Standardization (ISO)/International Electrotechnical Commission (IEC), College of American Pathologists (CAP), or similar certification. Presence of RET fusions detected on tests performed outside of LUNGMAP must have been confirmed by the study biomarker review panel
* Participants must be negative for all additional validated oncogenic drivers that could cause resistance to selpercatinib treatment. This includes EGFR sensitizing mutations, EGFR T790M mutations, ALK gene fusions, ROS1 gene fusion, KRAS activating mutations, BRAF V600E mutation and MET exon 14 skipping mutations or high-level amplification and expression

  * NOTE: EGFR, ALK, ROS, KRAS, and BRAF testing is performed as part of the LUNGMAP screening/pre-screening FoundationOne test. If prior data is not available, results from the FMI testing must be obtained prior to sub-study randomization.
* Participants must have measurable disease documented by computed tomography (CT) or magnetic resonance imaging (MRI). The CT from a combined positron emission tomography (PET)/CT may be used to document only non-measurable disease unless it is of diagnostic quality. Measurable disease must be assessed within 28 days prior to sub-study randomization. Pleural effusions, ascites and laboratory parameters are not acceptable as the only evidence of disease. Non-measurable disease must be assessed within 42 days prior to sub-study randomization. All disease must be assessed and documented on the Baseline Tumor Assessment Form. Participants whose only measurable disease is within a previous radiation therapy port must demonstrate clearly progressive disease (in the opinion of the treating investigator) prior to randomization
* Participants must have a CT or MRI scan of the brain to evaluate for central nervous system (CNS) disease within 42 days prior to sub-study randomization
* Participants must have received and developed disease progression during or after an anti-RET inhibitors treatment. The anti-RET inhibitor therapy must be the most recent therapy
* Participants must have progressed (in the opinion of the treating physician) following the most recent line of therapy
* Participants must have recovered (=\< grade 1) from any side effects of prior therapy. Participants must not have received any radiation therapy within 14 days prior to sub-study randomization
* For participants with stage IV or recurrent disease, the participant must not have received a platinum-based chemotherapy regimen. For participants whose prior systemic therapy was for stage I-III disease only (i.e., participant has not received any treatment for stage IV or recurrent disease), disease progression on platinum-based chemotherapy must not have occurred within one year (365 days) from the last date that the participant received that therapy. Prior anti-PD-1/PD-L1 therapy, alone or in combination (e.g., nivolumab, pembrolizumab, or durvalumab) is allowed
* Participants must have an electrocardiogram (ECG) performed within 28 days prior to sub-study randomization. It is suggested that a local cardiologist review the corrected QT by Fridericia's correction formula (QTcF) intervals
* Absolute neutrophil count (ANC) \>= 1.5 x 10\^3/uL obtained within 28 days prior to sub-study randomization
* Platelet count \>= 100 x 10\^3/uL obtained within 28 days prior to sub-study randomization
* Hemoglobin \>= 9 g/dL obtained within 28 days prior to sub-study randomization
* Serum bilirubin =\< institutional upper limit of normal (IULN) and either alanine aminotransferase (ALT) or aspartate aminotransferase (AST) =\< 2 x IULN within 28 days prior to sub-study randomization (if both ALT and AST are done, both must be \< 2 x IULN). For participants with liver metastases, bilirubin and either ALT or AST must be =\< 5 x IULN (if both ALT and AST are done, both must be =\< 5 x IULN)
* Participants must have a serum creatinine =\< the 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 sub-study randomization
* Participants must have Zubrod performance status 0-1 documented within 28 days prior to sub-study randomization
* Participants must provide pre-study history and physical exam within 28 days prior to sub-study 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 sub-study 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 28 days prior to sub-study randomization
* Participants with known human immunodeficiency virus (HIV) infection are eligible, provided they are on effective anti-retroviral therapy and have undetectable viral load at their most recent viral load test and within 6 months prior to sub-study randomization
* Participants must be able to swallow capsules
* Participants must agree to have blood specimens submitted for circulating tumor DNA (ctDNA)
* Participants must also be offered participation in banking and in the correlative studies for collection and future use of specimens
* Participants with impaired decision-making capacity are eligible as long as their neurological or psychological condition does not preclude their safe participation in the study (e.g., tracking pill consumption and reporting adverse events to the investigator)
* Participants 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

Exclusion Criteria:

* Participants must not have leptomeningeal disease, spinal cord compression or brain metastases unless: (1) metastases have been locally treated and have remained clinically controlled and asymptomatic for at least 14 days following treatment, and prior to sub-study randomization, AND (2) participant has no residual neurological dysfunction and has been off corticosteroids for at least 24 hours prior to sub-study randomization
* Participants must not have received any prior systemic therapy (systemic chemotherapy, tyrosine kinase inhibitor \[TKI\], immunotherapy or investigational drug) within 14 days prior to sub-study randomization
* Participants must not be planning to receive any concurrent chemotherapy, immunotherapy, biologic or hormonal therapy for cancer treatment while receiving treatment on this study. Concurrent use of hormones for non-cancer-related conditions (e.g., insulin for diabetes and hormone replacement therapy) is acceptable
* 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
* Participants must not have had a major surgery within 14 days prior to sub-study randomization. Participants must have fully recovered from the effects of prior surgery in the opinion of the treating investigator
* 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 6 months, or serious uncontrolled cardiac arrhythmia
* Participants must not be pregnant or nursing. Individuals who are of reproductive potential must have agreed to use an effective contraceptive method with details provided as a part of the consent process. A person who has had menses at any time in the preceding 12 consecutive months or who has semen likely to contain sperm is considered to be of "reproductive potential." In addition to routine contraceptive methods, "effective contraception" also includes refraining from sexual activity that might result in pregnancy and surgery intended to prevent pregnancy (or with a side-effect of pregnancy prevention) including hysterectomy, bilateral oophorectomy, bilateral tubal ligation/occlusion, and vasectomy with testing showing no sperm in the semen