A Study for Participants With Small-Cell Lung Cancer

Inclusion Criteria:

* Have histological or cytological evidence of extensive-disease small-cell lung cancer
* Have the presence of measurable disease as defined by the Response Evaluation Criteria in Solid Tumors (RECIST 1.1)
* Have received at least 1 prior chemotherapy regimen with agents known to provide clinical benefit for small-cell lung cancer and be, in the opinion of the investigator, an appropriate candidate for experimental therapy
* Have discontinued all previous therapies for cancer, including chemotherapy, biologic therapy, hormone therapy, or radiotherapy. Participants must have recovered from the acute effects of therapy (except alopecia and fatigue) before study enrollment
* Part A: Have a performance status of 0 to 2 on the Eastern Cooperative Oncology Group scale
* Part B: Have a performance status of 0 to 1 on the Eastern Cooperative Oncology Group scale

Exclusion Criteria:

* Have received treatment within 28 days of the first dose of LY2523355 with a drug that has not received regulatory approval for any indication
* Have a mixed histological diagnosis of small-cell lung cancer and non-small-cell lung cancer
* Have serious preexisting medical conditions that, in the opinion of the investigator, would preclude participation in this study
* Part A: Have symptomatic, untreated, or uncontrolled central nervous system (CNS) metastases. Participants with treated CNS metastases are eligible provided their disease is radiographically stable, asymptomatic, and corticosteroid use has been discontinued for at least 2 weeks prior to the first dose of study drug. Screening of asymptomatic participants without history of CNS metastases is not required
* Part B: Have symptomatic, untreated, or uncontrolled CNS metastases or a history of CNS metastases. Participants who have received prophylactic radiation are not excluded. Screening of asymptomatic participants without history of CNS metastases is not required