A Study of Ramucirumab (LY3009806) in Combination With Weekly Docetaxel in Participants With Stage IV Non-Small Cell Lung Cancer

Inclusion Criteria: * The participant had disease progression on or after prior platinum-based chemotherapy regimen for locally advanced or metastatic NSCLC. * Prior immunotherapy for NSCLC is allowed. * The participant has an Eastern Cooperative Oncology Group performance status of 0 or 1. * The participant has histologically or cytologically confirmed NSCLC. * The participant has metastatic NSCLC disease (Stage IV) at the time of first dose of study treatment. * The participant has measurable disease at the time of first dose of study treatment documented by computed tomography (CT) scan or magnetic resonance imaging (MRI). * The participant has resolution to Grade ≤1 by the National Cancer Institute-common terminology criteria for adverse events (NCI-CTCAE), Version 4.0, of all clinically significant toxic effects of prior locoregional therapy, surgery, or other anticancer therapy. * The participant has adequate organ function. * The participant's urine protein is \<2+ on dipstick or routine urinalysis (UA). If urine dipstick or routine analysis indicates proteinuria ≥2+, then a 24-hour urine must be collected and must demonstrate \<2 grams of protein in 24 hours to allow participation in the study. * For male participants, are sterile (including vasectomy confirmed by post vasectomy semen analysis) or agree to use a highly effective method of contraception (2 methods preferred, or per country requirements, whichever is more strict), and to not donate sperm starting with the first dose of study treatment, during the study, and for at least 6 months following the last dose of study treatment or country requirements, whichever is longer. * For female participants, are surgically sterile, postmenopausal, or agree to use a highly effective method of contraception (2 methods preferred, or per country requirements, whichever is more strict) during the study and for 6 months following the last dose of study treatment or country requirements, whichever is longer. * Female participants of childbearing potential must have a negative serum or urine pregnancy test within 72 hours prior to first dose of study treatment. * The participant has a life expectancy of ≥3 months. Exclusion Criteria: * Prior therapy with docetaxel or ramucirumab. * The participant has received more than 1 prior chemotherapy regimen for locally advanced or metastatic NSCLC; however, prior maintenance chemotherapy for locally advanced or metastatic NSCLC is allowed. * The participant's tumour contains small cell lung cancer. * The participant has undergone major surgery within 28 days prior to first dose of study treatment, or subcutaneous venous access device placement within 7 days prior to first dose of study treatment. Furthermore, any participant with postoperative bleeding complications or wound complications from a surgical procedure performed in the last 2 months will be excluded. * The participant has a bowel obstruction, history or presence of inflammatory enteropathy or extensive intestinal resection (hemicolectomy or extensive small intestine resection with chronic diarrhea), Crohn's disease, ulcerative colitis, or chronic diarrhea. * The participant has peripheral neuropathy Grade ≥2 (NCI-CTCAE v 4.0). * The participant has an elective or a planned major surgery during the course of the trial. * The participant is receiving concurrent treatment with other anticancer therapy, including other chemotherapy, immunotherapy, hormonal therapy, chemoembolization, or targeted therapy. * The participant has symptomatic, active, or untreated central nervous system (CNS) metastases. Brain metastases that are asymptomatic, stable and not requiring steroid use, and previously treated by radiation are allowed. The participant may have no evidence of Grade ≥1 CNS hemorrhage based on pretreatment MRI or I.V. contrast CT scan (performed within 21 days before first dose of study treatment). * The participant has radiologically documented evidence of major blood vessel invasion or encasement by cancer. * The participant has radiographic evidence of intratumor cavitation, regardless of tumor histology. * The participant has a history of uncontrolled hereditary or acquired thrombotic disorder. * The participant is receiving chronic therapy with nonsteroidal anti-inflammatory drugs (NSAIDs; for example, indomethacin, ibuprofen, naproxen, or similar agents) or other antiplatelet agents (for example, clopidogrel, ticlopidine, dipyridamole, and anagrelide). Aspirin (acetylsalicylic acid) use at doses up to 325 milligrams/day is permitted. * Participants with a history of gross hemoptysis (defined as bright red blood or ≥1/2 teaspoon) within 2 months prior to first dose of study treatment. * The participant has clinically relevant congestive heart failure (New York Heart Association Class II-IV) or symptomatic or poorly controlled cardiac arrhythmia. * The participant has experienced any arterial thrombotic event, including myocardial infarction, unstable angina, cerebrovascular accident, or transient ischemic attack, within 6 months prior to first dose of study treatment. * The participant has uncontrolled arterial hypertension ≥150 / ≥90 millimeters of mercury despite standard medical management. * The participant has had a serious or nonhealing wound, ulcer, or bone fracture ≤28 days prior to first dose of study treatment. * The participant has significant bleeding disorders, vasculitis, or experienced Grade 3-4 gastrointestinal (GI) bleeding within 3 months prior to first dose of study treatment. * History of GI perforation and / or fistulae within 6 months prior to first dose of study treatment.