A Study of LY2510924 in Participants With Extensive-Stage Small Cell Lung Carcinoma

Inclusion Criteria: * histologically or cytologically confirmed extensive-stage disease small cell lung carcinoma * measurable disease as defined by the New Response Evaluation Criteria in Solid Tumors (RECIST): Revised RECIST Guideline (version 1.1) * no prior systemic chemotherapy, immunotherapy, biological, hormonal, or investigational therapy for SCLC * a performance status of 0-2 on the Eastern Cooperative Oncology Group (ECOG) scale * adequate organ function, including: * hematologic: absolute neutrophil (segmented and bands) count (ANC) greater than or equal to (≥)1.5 x 10\^9/ liter (L), platelets ≥100 x 10\^9/L, and hemoglobin ≥9 grams per deciliter (g/dL). * hepatic: bilirubin less than or equal to (≤)1.5 times upper limits of normal (ULN), and alkaline phosphatase (AP), alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤3.0 times ULN (AP, AST, and ALT ≤5 times ULN is acceptable if liver has tumor involvement * renal: calculated creatinine clearance (CrCl) ≥45 milliliters per minute (mL/min) based on the standard Cockcroft and Gault formula * For women: Must be surgically sterile (surgical procedure: bilateral tubal ligation), post-menopausal (at least 12 consecutive months of amenorrhea), or compliant with a medically approved contraceptive regimen (intrauterine device \[IUD\], birth control pills, or barrier device) during and for 6 months after the treatment period; must have a negative serum or urine pregnancy test within 7 days before study enrollment, and must not be breast-feeding. For men: Must be surgically sterile or compliant with a contraceptive regimen during and for 6 months after the treatment period. * estimated life expectancy of at least 12 weeks * written informed consent prior to any study-specific procedures * able and willing to learn to self-administer LY2510924, or have a caregiver who is willing to learn and able to administer LY2510924 by subcutaneous (SC) injection Exclusion Criteria: * 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 * prior treatment with carboplatin/etoposide or LY2510924 * any concurrent administration of any other antitumor therapy * diagnosis of non-small cell lung cancer (NSCLC) or mixed NSCLC and small cell lung cancer (SCLC) * no prior malignancy other than SCLC, carcinoma in situ of the cervix, or nonmelanoma skin cancer, unless that prior malignancy was diagnosed and definitively treated 5 or more years prior to study entry with no subsequent evidence of recurrence. Participants with a history of low grade (Gleason score ≤6) localized prostate cancer will be eligible even if diagnosed less than 5 years prior to study entry * serious concomitant systemic disorder that, in the opinion of the investigator, would compromise the participant's ability to adhere to the study requirements * active or ongoing infection during screening requiring the use of systemic antibiotics * serious cardiac condition, such as myocardial infarction within 6 months, angina, or heart disease as defined by the New York Heart Association Class III or IV * clinical evidence of central nervous system (CNS) metastases or leptomeningeal carcinomatosis, except for individuals who have previously- treated central nervous system (CNS) metastases, are asymptomatic, and have had no requirement for steroid medication for 1 week prior to the first dose of study drug and have completed radiation 2 weeks prior to the first dose of study drug. * known or suspected allergy to any agent given in association with this trial * pregnant or lactating women