A Study of LOXO-435 in Participants With Cancer With a Change in a Gene Called FGFR3

Inclusion Criteria: Have solid tumor cancer with an FGFR3 pathway alteration on molecular testing in tumor or blood sample that is deemed as actionable. Cohort A1 (Dose Escalation): Presence of an alteration in FGFR3 or its ligands. Cohort A2 (Dose Optimization): Histological diagnosis of urothelial cancer (UC) that is locally advanced or metastatic with a qualifying FGFR3 alteration. Cohorts B1, B2 and B3 (Dose Expansion): Histological diagnosis of urothelial cancer that is locally advanced or metastatic with a prespecified activating FGFR3 alteration. Cohort C (Dose Expansion): Must have histological diagnosis of a non-urothelial solid tumor malignancy that is locally advanced or metastatic with a prespecified activating FGFR3 alteration. Measurability of disease: Cohort A1: Measurable or non-measurable disease as defined by Response Evaluation Criteria in Solid Tumors v 1.1 (RECIST v1.1) Cohorts A2, B1, B2, B3, and C1: Measurable disease required as defined by RECIST v1.1 Have adequate archival tumor tissue sample available or undergo a screening biopsy if allowed per country-specific regulations. Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. Prior Systemic Therapy Criteria: Cohort A1/C1: Participant has received all standard therapies for which the participant was deemed to be an appropriate candidate by the treating Investigator; OR the participant is refusing the remaining most appropriate standard of care treatment; OR there is no standard therapy available for the disease. There is no restriction on number of prior therapies. Cohort A2/B1/B2/B3: Participants must have received at least one prior regimen in the advanced or metastatic setting. There is no restriction on number of prior therapies. FGFR inhibitor specific requirements: Cohort A1/A2: Prior FGFR inhibitor treatment is permitted, but not required. Cohort B1: Participants must have been previously treated with a FGFR inhibitor. Cohort B2, B3, C1: Participants must be FGFR inhibitor naïve. Exclusion Criteria: Participants with primary central nervous system (CNS) malignancy. Known or suspected history of uncontrolled CNS metastases. Current evidence of corneal keratopathy or retinal disorder. Have a history and/or current evidence of extensive tissue calcification. Any serious unresolved toxicities from prior therapy. Significant cardiovascular disease. Prolongation of the QT interval corrected for heart rate using Fridericia's formula (QTcF). Active uncontrolled systemic infection or other clinically significant medical conditions. Participants who are pregnant, lactating, or plan to breastfeed during the study or within 6 months of the last dose of study treatment. Participants who have stopped breastfeeding may be enrolled.