A Study of LY3039478 in Participants With Advanced Cancer

The purpose of this study is to find a recommended dose level of LY3039478 that can safely be taken by participants with advanced cancer or cancer that has spread to other parts of the body, including but not limited to lymphoma. The study will also explore changes to various markers in blood cells and tissue. Finally, the study will help to document any tumor activity this drug may have.

In Part A of this study, participants with advanced/metastatic cancer (including lymphoma) will receive increasing doses of LY3039478 to define the dose level for Part B, C, D and E. In Part B, C, D and E LY3039478 will be explored at a predefined fixed dose level. Participants in Part B and D must have a defined alteration in a certain molecular pathway. Enrollment of participants in Part B, C, D and E will start once Part A is completed. In Part F participants will receive increasing doses of LY3039478 in combination with prednisone to define the maximum tolerated dose level.

Eligibility Criteria:
Inclusion Criteria:

* For all parts: The participant must be, in the judgment of the investigator, an appropriate candidate for experimental therapy after available standard therapies have failed to provide clinical benefit for their advanced or metastatic cancer.
* For Dose Escalation (Part A): The participant must have histological or cytological evidence of cancer, either a solid tumor or a lymphoma, which is advanced or metastatic.
* For Part B: All participants must have a histological evidence of their advanced or metastatic cancer and prescreened alterations in a defined pathway.
* For Part C: All participants must have histological evidence of advanced or metastatic specific subtypes of soft tissue sarcoma.
* For Part D: All participants must have histological evidence of advanced or metastatic cancer and prescreened alterations in a defined pathway.
* Cohort 1: Participants must have triple negative breast cancer.
* Cohort 2: Participants must have hepatocellular carcinoma (HCC). These participants should have Child-Pugh stage A.
* Cohort 3: Participants must have cholangiocarcinoma.
* Cohort 4: Participants must have chronic lymphocytic leukemia.
* Cohort 5: Participants must have a mature T cell, B cell, or natural killer (NK) cell neoplasm.
* For Part E: Participants must have adenoid cystic carcinoma (ACC).
* For Part F dose confirmation: Participants must have leiomyosarcoma and prescreened alterations in a defined pathway.
* As defined by the Response Evaluation Criteria in Solid Tumors (RECIST 1.1), the Revised Response Criteria for Malignant Lymphoma or the Response Assessment in Neuro Oncology (RANO) criteria for glioblastoma:

  * For Dose Escalation (Part A): Have measurable or nonmeasurable disease.
  * For Parts B, C, D, E and F: Have measurable disease or reliable biomarker measure.
* For Parts B, C, D, E and F: Have available tumor tissue.
* Have adequate organ function.
* Have a performance status of less than or equal to 1 on the Eastern Cooperative Oncology Group (ECOG) scale and life expectancy of more than 12 weeks.

Exclusion Criteria:

* Have symptomatic or non stable central nervous system (CNS) malignancy.
* Females who are pregnant or lactating.
* Have active bacterial, fungal, and/or known viral infection.
* Have malabsorptive syndromes, enteropathies, gastroenteritis (acute or chronic), or diarrhea (acute or chronic).
* Participants with HCC that:

  * Have known HCC with fibro-lamellar or mixed histology.
  * Have presence of clinically relevant ascites.
  * Have had a liver transplant.
  * Have active or uncontrolled clinically serious hepatitis B virus or hepatitis C virus infection.