Phase 2 Cohorts 1 and 2: an additional known oncogenic driver Cohorts 3 and 4: Enrollment closed Cohorts 1, 2 and 5: prior treatment with a selective RET inhibitor Notes: Participants otherwise eligible for Cohorts 1, 2, and 5 who discontinued another selective RET inhibitor may be eligible for Phase 2 Cohort 6 with prior Sponsor approval - Investigational agent or anticancer therapy (including chemotherapy, biologic therapy, immunotherapy, anticancer Chinese medicine or other anticancer herbal remedy) within 5 half-lives or 2 weeks (whichever is shorter) prior to planned start of LOXO-292 (selpercatinib). In addition, no concurrent investigational anti-cancer therapy is permitted Note: Potential exception for this exclusion criterion will require a valid scientific justification and approval from the Sponsor - Major surgery (excluding placement of vascular access) within 2 weeks prior to planned start of LOXO-292 (selpercatinib) - Radiotherapy with a limited field of radiation for palliation within 1 week of planned start of LOXO-292 (selpercatinib), with the exception of participants receiving radiation to more than 30% of the bone marrow or with a wide field of radiation, which must be completed at least 4 weeks prior to the first dose of study treatment - Any unresolved toxicities from prior therapy greater than Common Terminology Criteria for Adverse Events (CTCAE) Grade 1 at the time of starting study treatment with the exception of alopecia and Grade 2, prior platinum-therapy related neuropathy - Symptomatic primary CNS tumor, metastases, leptomeningeal carcinomatosis, or untreated spinal cord compression. Participants are eligible if neurological symptoms and CNS imaging are stable and steroid dose is stable for 14 days prior to the first dose of LOXO-292 (selpercatinib) and no CNS surgery or radiation has been performed for 28 days, 14 days if stereotactic radiosurgery (SRS) - Clinically significant active cardiovascular disease or history of myocardial infarction within 6 months prior to planned start of LOXO-292 (selpercatinib) or prolongation of the QT interval corrected (QTcF) greater than (>) 470 milliseconds (msec) • Participants with implanted pacemakers may enter the study without meeting QTc criteria due to nonevaluable measurement if it is possible to monitor for QT changes. • Participants with bundle branch block may be considered for study entry if QTc is appropriate by a formula other than Fridericia's and if it is possible to monitor for QT changes. - Required treatment with certain strong cytochrome P450 3A4 (CYP3A4) inhibitors or inducers and certain prohibited concomitant medications - Phase 2 Cohort 7 (neoadjuvant treatment): Participant must not have received prior systemic therapy for NSCLC.