The objective of this study is to determine a recommended Phase 2 dose range of LY2875358 that may be safely administered to participants with advanced cancer. In Part A and Part A2 of this study, escalating doses of LY2875358 as monotherapy and in combination with erlotinib will be evaluated for safety and tolerability, respectively. Part B is a dose-confirmation segment for LY2875358 therapy in 5 different types of cancer: nonsquamous non-small cell lung cancer (NSCLC), castrate resistant prostate cancer (CRPC) with bone metastases, renal cell carcinoma (RCC), hepatocellular carcinoma (HCC), or uveal melanoma with liver metastases, and for LY2875358 in combination with trametinib in participants with uveal melanoma with liver metastases.

Protocol amendment (November, 2013) expanded Part B to study LY2875358 in combination with trametinib in participants with uveal melanoma with liver metastasis.

Inclusion Criteria:

• Part A: Have histological or cytological evidence of cancer (solid tumor, lymphoma, or multiple myeloma) that is advanced and/or metastatic and an appropriate candidate for experimental therapy

• Part A2: Histologic or cytologic diagnosis of advanced Non Small Cell Lung Cancer (NSCLC), Stage IIIB with malignant pleural effusion or Stage IV, completed at least 1 prior systemic regimen, and eligible for erlotinib therapy.

• Part B: Candidate for experimental therapy after standard therapies used or non-eligible for standard therapies. Histological or cytological evidence of 1 of the 5 tumor types:

• Castrate-resistant prostate cancer (CRPC) with bone metastasis:

  --Progressive Disease in the setting of castrate level of testosterone

• Renal Cell Carcinoma (RCC):

  --Histologic diagnosis of either clear-cell or papillary RCC (metastatic and unresectable, or bilateral, multifocal, unresectable RCC localized to kidneys).

• NSCLC:

  --Histologic or cytologic diagnosis of advanced NSCLC, Stage IIIB with malignant pleural effusion or Stage IV

• Hepatocellular Carcinoma (HCC)

  --Histologic or cytologic diagnosis of hepatocellular carcinoma

• Uveal Melanoma with liver metastasis

• Part A: Have the presence of measurable or nonmeasurable disease as defined by the RECIST v1.1 (Eisenhauer et al. 2009) or Revised Response Criteria for Malignant Lymphoma (Cheson et al. 2007) or have measureable disease for multiple myeloma.

• Part A2 & B (RCC, NSCLC, HCC, and uveal melanoma): Have measurable disease as defined by RECIST v1.1.

• Give written informed consent prior to any study-specific procedures.

• Adequate organ function.

• Performance status of less than or equal to 2 on ECOG scale.

• Discontinued all previous cancer therapies, and any agents that have not received regulatory approval, for at least 21 days and recovered from the acute effects of therapy. Must have discontinued mitomycin-C or nitrosourea therapy for at least 42 days.

• Reliable and available for the duration of the study and willing to follow study procedures.

• Males and females (reproductive potential): Use medically approved contraceptive precautions during the study and for 4 months following the last dose of study drug.

• Females (childbearing potential): Have had a negative serum pregnancy test before the first dose of study drug and not be breast-feeding.

• Estimated life expectancy that will permit the participants to complete 8 weeks of treatment.

Exclusion Criteria:

• Serious preexisting medical conditions

• Symptomatic central nervous system malignancy or metastasis (screening not required).

• Acute or chronic leukemia.

• Active infection including HIV, hepatitis A, B or C

• Have second primary malignancy that may affect the interpretation of results.

• Have received a liver transplant, or have liver cirrhosis with a Child-Pugh Stage of B or C.

• Patients with active alcohol abuse, as determined by the treating investigator.

• Part A2: Unable to swallow tablets. Intolerant of therapy with erlotinib. Concomitant treatment with the cytochrome P450 3A (CYP3A) modulators. Must not have received treatment with any of these modulators within 14 days of study treatment.

• Have a history of New York Heart Association class ≥3, unstable angina, myocardial infarction 6 months prior to study drug

• QTc greater than 470 msec.

• Received previous treatment with any c-MET experimental therapeutic.

• Part B Expansion Cohort 1 (CRPC):

  1. Increasing use of daily doses of opioid analgesics within 28 days prior to enrollment in the study.
  2. Neuroendocrine prostate cancer.
  3. Patients who have a solitary bone metastasis that has been irradiated are not eligible.

• Part B Expansion Cohort 6 (LY2875358 plus trametinib in participants with uveal melanoma with liver metastasis): Contra-indications for trametinib