Key Inclusion Criteria:

        For Phase 1:

          -  Participants with a locally advanced or metastatic solid tumor that:

          -  Has progressed on or is intolerant to standard therapy, or

          -  For which no standard therapy exists, or in the opinion of the Investigator, are not
             candidates for or would be unlikely to tolerate or derive significant clinical benefit
             from standard therapy, or

          -  Decline standard therapy

          -  Prior multikinase inhibitors (MKIs) with anti-RET activity are allowed

          -  A RET gene alteration is not required initially. Once adequate PK exposure is
             achieved, evidence of RET gene alteration in tumor and/or blood is required as
             identified through molecular assays, as performed for clinical evaluation

          -  Measurable or non-measurable disease as determined by RECIST 1.1 or RANO as
             appropriate to tumor type

          -  Eastern Cooperative Oncology Group (ECOG) score of 0, 1, or 2 or Lansky Performance
             Score (LPS) greater than or equal to (≥) 40 percent (%) (age less than [<] 16 years)
             with no sudden deterioration 2 weeks prior to the first dose of study treatment

          -  Adequate hematologic, hepatic and renal function

          -  Life expectancy of at least 3 months

        For Phase 2: As for phase 1 with the following modifications:

          -  For Cohort 1: Participants must have received prior standard therapy appropriate for
             their tumor type and stage of disease, or in the opinion of the Investigator, would be
             unlikely to tolerate or derive clinical benefit from appropriate standard of care
             therapy

          -  Cohorts 1 and 2:

               -  Enrollment will be restricted to participants with evidence of a RET gene
                  alteration in tumor

               -  At least one measurable lesion as defined by RECIST 1.1 or RANO, as appropriate
                  to tumor type and not previously irradiated

          -  Cohorts 3 and 4: Enrollment closed

          -  Cohort 5:

               -  Without measurable disease but otherwise meet criteria for Cohorts 1 and 2;

               -  MTC syndrome spectrum cancers (e.g., MTC, pheochromocytoma), cancers with
                  neuroendocrine features/differentiation, or poorly differentiated thyroid cancers
                  with other RET alteration/activation may be allowed with prior Sponsor approval;

               -  cfDNA positive for a RET gene alteration not known to be present in a tumor
                  sample

          -  Cohort 6: Participants who otherwise are eligible for Cohorts 1, 2 or 5 who
             discontinued another RET inhibitor due to intolerance may be eligible with prior
             Sponsor approval

          -  Cohort 7: Participants must have a histologically confirmed stage IB-IIIA NSCLC by
             AJCC (The American Joint Committee on Cancer) version 8. The tumor must have been
             deemed resectable by a thoracic surgeon, the participant must be determined to be
             medically operable based on the determination of a thoracic surgeon, and the
             participant must not have received prior systemic therapy, including prior radiation
             therapy, for NSCLC.

        Key Exclusion Criteria (Phase 1 and Phase 2):

          -  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 4 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)

          -  Required treatment with certain strong cytochrome P450 3A4 (CYP3A4) inhibitors or
             inducers and certain prohibited concomitant medications