The purpose of this study is to assess the safety and tolerability of LY2875358 in Japanese participants with cancer that is advanced and/or may have spread to another part of the body.

This study has 3 parts. Participants may only enroll in one part.

Part A - Participants will receive LY2875358.

Part B1 - Participants with non-small cell lung cancer (NSCLC) will receive LY2875358 and erlotinib.

Part B2 - Participants with NSCLC will receive LY2875358 and gefitinib.

Parts B1 and B2 were added per protocol amendment in January, 2013.

Inclusion Criteria:

• Part A: Have histological or cytological evidence of malignancies (solid tumor or lymphoma) that are advanced and/or metastatic. The participant must be, in the judgment of the investigator, an appropriate candidate for experimental therapy after available standard therapies have been used
• Part B1: Have histologic or cytologic diagnosis of advanced NSCLC, Stage IV per the 7th edition of the American Joint Committee on Cancer (AJCC) Staging Criteria for NSCLC. The participants must have no other effective therapeutic option and be eligible for erlotinib therapy per Japanese package insert in the opinion of investigator
• Part B2: Have histologic or cytologic diagnosis of advanced NSCLC with epidermal growth factor receptor (EGFR) activating mutation, Stage IV per the 7th edition of the AJCC Staging Criteria for NSCLC. The participants must have no other effective therapeutic option and be eligible for gefitinib therapy per Japanese package insert in the opinion of investigator
• Have the presence of measurable or nonmeasurable disease as defined by the Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1 or Revised Response Criteria for Malignant Lymphoma
• Have adequate hematologic, hepatic and renal function
• Have a performance status of ≤2 on the Eastern Cooperative Oncology Group (ECOG) scale
• Have discontinued all previous cancer therapies, and any agents that have not received regulatory approval for any indication, for at least 21 days or 5 half lives prior to study enrollment, whichever is shorter, and recovered from the acute effects of therapy (treatment-related toxicity resolved to baseline or ≤ Grade 1). Participants must have discontinued mitomycin-C or nitrosourea therapy for at least 42 days
• Males and females with reproductive potential: Must agree to use medically approved contraceptive precautions during the study and for 4 months following the last dose of study drug or until in the judgment of the investigator, it is safe for the participant to become pregnant
• Females with child bearing potential: Have had a negative urine pregnancy test ≤7 days before the first dose of study drug and must also not be breastfeeding. If female who stop breastfeeding enter the study, the female must stop breastfeeding from the day of the first study drug administration until 4 months after the last dose
• Have an estimated life expectancy, in the judgment of the investigator, that will permit the participant to complete 8 weeks of treatment

Exclusion Criteria:

• Have serious preexisting medical conditions
• Part A: Have symptomatic central nervous system malignancy or metastasis
• Part B: Have brain metastases that are symptomatic or require ongoing treatment with steroids or radiation therapy
• Have current acute or chronic leukemia (participants with adult T-cell leukemia/lymphoma are eligible)
• Have an active fungal, bacterial, and/or known viral infection
• Have a second primary malignancy that in the judgment of the investigator and sponsor may affect the interpretation of results
• Have a history of New York Heart Association (NYHA) class ≥3, unstable angina, myocardial infarction in 6 months prior to study drug administration
• Have QTc interval of >470 milliseconds (msec) on screening electrocardiogram
• Have received a liver transplant, or have liver cirrhosis with a Child-Pugh Stage of B or C
• Participants with active alcohol abuse, as determined by the treating investigator
• Previous treatment with any extracellular domain of mesenchymal-epithelial transition factor (c-MET) targeting experimental therapeutic (for example, XL184, ARQ197, or onartuzumab)
• Have a history of radiation therapy involving more than 25% of the bone marrow. Previous radiation therapy is allowed but should have been limited and must not have included whole pelvis radiation
• Part B: The participants actively receiving warfarin therapy at the time of enrollment
• Part B: Concomitant treatment with the cytochrome P450 (CYP) 3A4 modulators. The participants must not have received treatment with any of these modulators within 14 days of Cycle 1 Day 1
• Part B: Have any evidence of clinically active interstitial lung disease (ILD). Asymptomatic participants with chronic, stable, radiographic changes are eligible
• Part B: Have preexisting interstitial lung disease risks as evidenced by computed tomography (CT) scan/X-ray at baseline; have or had any disease of acute lung injury, idiopathic pulmonary fibrosis, pneumonitis, or pneumoconiosis evident on an x-ray; have or had any disease of radiation pneumonia or drug-induced pneumonia, which requires treatment with corticosteroids
• Part B: Have previously been intolerant of therapy with erlotinib or gefitinib