The primary purpose of this study is to compare the efficacy of the study drug LY2875358, given together with erlotinib, against erlotinib, alone. Participants will have Non-Small Cell Lung Cancer (NSCLC) that has advanced to Stage IV. Participants should not have been treated with drugs for Stage IV NSCLC, previously. All participants will get erlotinib alone, for approximately 8 weeks. Participants with radiographic disease control at the end of the erlotinib lead-in study period will be randomly assigned to receive LY2875358 plus erlotinib or erlotinib alone. Participants, who were chosen to receive erlotinib, alone, may cross over to the combination treatment at the time of progression.

Inclusion Criteria:

• Histologically or cytologically confirmed diagnosis of metastatic Stage IV NSCLC
• Have at least 1 measurable lesion whose presence is assessable using standard techniques by Response Evaluation Criteria in Solid Tumors (RECIST version 1.1)
• Have molecular evidence of an epidermal growth factor receptor mutation (EGFRmt) known to be associated with EGFR tyrosine kinase inhibitor (TKI) drug sensitivity (G719X, exon 19 deletion, L858R, L861Q)
• Eastern Cooperative Oncology Group (ECOG) performance status of ≤ 2
• Haven't received any prior systemic chemotherapy for Stage IV NSCLC (unless received as neoadjuvant or adjuvant therapy for early-stage NSCLC disease and completed therapy at least 6 months prior to enrollment)
• Availability of adequate tumor material (block or slides)

Exclusion Criteria:

• Are currently enrolled in, or discontinued within the last 30 days from, a clinical trial involving an investigational product or non-approved use of a drug or device
• Have previously completed or withdrawn from this study or any other study investigating LY2875358
• Have a serious concomitant systemic disorder or significant cardiac disease
• Have interstitial pneumonia or interstitial fibrosis of the lung or have pleural effusion, pericardial fluids or ascites, requiring drainage every other week or more frequently
• Have a history of another malignancy except for basal or squamous cell skin cancer and/or in situ carcinoma of the cervix, or other solid tumors treated curatively and without evidence of recurrence for at least 3 years prior to the study
• Have major surgery less than 2 weeks prior to the initiation of study treatment therapy
• Pregnant or lactating women

Anonymized individual patient level data will be provided in a secure access environment upon approval of a research proposal and a signed data sharing agreement.

Data are available 6 months after the primary publication and approval of the indication studied in the US and European Union (EU), whichever is later. Data will be indefinitely available for requesting.

A research proposal must be approved by an independent review panel and researchers must sign a data sharing agreement.