The main purpose of this study is to evaluate tolerability of merestinib monotherapy or in combination with other anti-cancer agents in Japanese participants with advanced and/or metastatic cancer.

Inclusion Criteria:

• Part A: Histological or cytological evidence of a diagnosis of cancer that is advanced and/or metastatic (solid tumors or non-Hodgkin's lymphoma).
• Part B: Biliary tract carcinoma that is unresectable, recurrent, or metastatic. The participant must not have received prior systemic front-line therapy for metastatic or resectable disease.
• Part A: Measurable or nonmeasurable disease as defined by Response Evaluation Criteria in Solid Tumors (RECIST) v1.1 or Cheson Criteria.
• Part B: Measurable disease as defined by RECIST v1.1.
• Adequate organ function including hematologic, hepatic and renal.
• Eastern Cooperative Oncology Group (ECOG) scale of 0 or 1.
• Are able to swallow tablets.
• For participants in Part B, a tumor tissue sample is mandatory for biomarker analysis.
• Males must agree to use medically approved barrier contraceptive precautions during the study and for 3 months following the last dose of study drug.
• Females with childbearing potential: Must agree to use medically approved contraceptive precautions during the study and for 3 months following the last dose of study drug, must have had a negative serum or urine pregnancy test ≤7 days before the first dose of study drug.
• A breastfeeding woman must not be breastfeeding. If a female who stops breastfeeding enters the study, breastfeeding must cease from the day of the first study drug administration until at least 3 months after the last administration.

Exclusion Criteria:

• Have serious pre-existing medical conditions.
• Have a chronic underlying infection.
• Have symptomatic central nervous system malignancy or metastasis.
• Have an active fungal, bacterial, and/or known viral infection.
• Part B: Have mixed hepatocellular biliary tract carcinoma histology.
• Have liver cirrhosis with a Child-Pugh stage of B or higher, or have received a liver transplant.
• Have a history of congestive heart failure with New York Heart Association (NYHA) class greater than 2, unstable angina, or have recent history of myocardial infarction, transient ischemic attacks, stroke, or arterial or venous vascular disease.
• Have a corrected QT interval >470 milliseconds as calculated be the Fredericia equation.
• Have a second primary malignancy that, in the judgment of the investigator, and sponsor may affect the interpretation of results.
• Have any evidence of clinically active interstitial lung disease (ILD).