A Study of Pemetrexed and Gefitinib Versus Gefitinib in Non-Small Cell Lung Cancer (NSCLC)

Inclusion Criteria: * Histologically or cytologically confirmed advanced (Stage IV) or recurrent non-squamous NSCLC * Eligible participants of reproductive potential must agree to use adequate contraceptive methods during the study period and for at least 6 months after the last dose of study therapy * Negative pregnancy test for women of childbearing potential * Males or females, aged 18 years or above * Eastern Cooperative Oncology Group (ECOG) Performance Status 0-1 * The participant's primary NSCLC tumor has an activating Epidermal Growth Factor Receptor (EGFR) mutation, as determined by any validated method * The participant consents to provide a tissue sample for prestudy EGFR mutation testing and the tumor tissue sample is available for detection of EGFR expression and other markers for centralized testing by Lilly * The participant has measurable disease at the time of study entry, documented by computed tomography (CT) scan or magnetic resonance imaging (MRI), as defined by the Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1 * The participant has not had any prior systemic chemotherapy, immunotherapy, or biological therapy (for example, targeted therapy, such as erlotinib or gefitinib) for Stage IV or recurrent non-squamous NSCLC * The participant has adequate organ function, defined as: * White blood cell count ≥3 x 10\^9/liter (L); absolute neutrophil count (segmented and bands) ≥1.5 x 10\^9/L; platelet count ≥100 x 10\^9/L; hemoglobin ≥9.0 gram per deciliter (g/dL) * Total bilirubin ≤1.5 times the upper limit of the normal (ULN) range; and alkaline phosphatase (AP), aspartate transaminase (AST) and alanine transaminase (ALT) ≤2.5 times ULN (or ≤5 times ULN if the liver has tumor involvement) * Calculated creatinine clearance ≥45 milliliter per minute (mL/min) * The participant is able to take folic acid, vitamin B12, and dexamethasone, according to the protocol's requirements * Life expectancy of at least 3 months * Provision of informed consent * Prior radiation therapy is allowed to \<25% of the bone marrow; however, prior radiation to the whole pelvis not allowed. Prior radiation therapy must be completed at least 2 weeks prior to first study-drug administration. Participants must have recovered from the acute toxic effects prior to first study-drug administration. Exclusion Criteria: * The participant has received prior chemotherapy for advanced and/or metastatic disease, or adjuvant/neoadjuvant treatment with pemetrexed or an EGFR-tyrosine Kinase inhibitor (TKI) * The participant's tumor contains predominantly small cell lung cancer or squamous NSCLC * The participant is receiving concurrent treatment with any other anticancer therapy, including other chemotherapy, immunotherapy, hormonal therapy, chemoembolization, biological or targeted therapy, or radiotherapy (palliative irradiation of bone lesions is allowed) * The participant has untreated central nervous system (CNS) metastases Participants with treated brain metastases are eligible if they are clinically stable with regard to neurologic function, off steroids after cranial irradiation (whole brain radiation therapy, focal radiation therapy, stereotactic radiosurgery) ending at least 2 weeks before enrollment, or after surgical resection performed at least 28 days before enrollment. No evidence of Grade ≥1 CNS hemorrhage based on pretreatment MRI or Intravenous (IV) contrast CT scan (performed within 21 days before randomization). * The participant has undergone radiotherapy within 28 days before enrollment (localized radiotherapy for pain relief allowed, provided 25% or less of their total bone marrow had been irradiated) * The participant has clinically relevant congestive heart failure (New York Heart Association \[NYHA\] II-IV) or symptomatic or poorly controlled cardiac arrhythmia * The participant has a serious illness or medical condition that would compromise their safety or impair their ability to comply with the protocol's requirements, including, but not limited to, the following: * Known human immunodeficiency virus (HIV) infection or acquired immunodeficiency syndrome (AIDS)-related illness * Active or uncontrolled clinically serious infection * Previous or concurrent 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 5 years prior to the study * Uncontrolled metabolic disorders or other nonmalignant organ or systemic diseases or secondary effects of cancer that induce a high medical risk and/or make assessment of survival uncertain * Other severe acute or chronic medical or psychiatric condition or laboratory abnormality that may increase the risk associated with study participation or study drug administration, or may interfere with the interpretation of study results, and in the judgment of the Investigator would make the participant ineligible for entry into this study * The participant has significant third space fluid retention, and is not amenable for required repeated drainage * Known allergy or hypersensitivity reaction to any of the treatment components * Are unable to interrupt aspirin or other non-steroidal anti-inflammatory drugs (NSAIDs), other than an aspirin dose ≤1.3 grams per day, for at least 2 days (5 days for long-acting agents \[for example, piroxicam\]) before, during, and for at least 2 days after administration of pemetrexed * Concomitant use of cytochrome P450 (CYP)3A4 inducers or CYP3A4 inhibitors * Participants under therapy with warfarin or coumarin derivatives who are unable to switch to low molecular weight heparin, unless regular monitoring of changes in prothrombin time (PT) (PT/international normalized ratio \[INR\]) will be applicable * Any known significant ophthalmologic abnormalities of the surface of the eye. The use of contact lenses is not recommended during the study * 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, or concurrently enrolled in any other type of medical research judged not to be scientifically or medically compatible with this study Participants participating in surveys or observational studies are eligible to participate in this study * The participant has previously received treatment with gefitinib, erlotinib or pemetrexed * Any evidence of clinically active interstitial lung disease. Asymptomatic participants with chronic, stable, radiographic changes are eligible. * Have preexisting idiopathic pulmonary fibrosis as evidenced by computed tomography (CT) scan/x-ray at baseline; have or had any disease of acute lung injury, idiopathic pulmonary fibrosis, pulmonary pneumonia, or pneumoconiosis evident on an x-ray; have or had any disease of radiation pneumonia or drug-induced pneumonia, which requires treatment with corticosteroids. * The participant is pregnant or breastfeeding