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. Patients 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. Patients 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 patients without history of CNS metastases is not required

- Part B: Have symptomatic, untreated, or uncontrolled central nervous system (CNS)
metastases or a history of CNS metastases. Patients who have received prophylactic
radiation are not excluded. Screening of asymptomatic patients without history of CNS
metastases is not required