A Study of Advanced or Metastatic Non-small Cell Lung Cancer

Inclusion Criteria:

Must agree to have a tumor biopsy at screening
Must have a diagnosis of advanced or metastatic non-squamous non-small cell lung cancer that has progressed after certain prior treatment
Must be available for the duration of the study and willing to follow the study procedures
If participant is a woman that is capable of having children, must have a negative pregnancy test within 7 days of taking first dose of study drug
Must have discontinued radiation therapy at least 4 weeks before entering this study

Exclusion Criteria:

Must not have taken an unapproved drug as treatment for any indication within the last 28 days before starting study treatment.
Must not be pregnant or lactating, are considering becoming pregnant, or are considering fathering a child. Males and females with reproductive potential must agree to use medically approved contraceptive precautions during the trial until the participant's physician considers it safe to become pregnant or father a child.
Must not have known positive test in human immunodeficiency virus (HIV), hepatitis B surface antigen (HBSAg), or hepatitis C antibodies (HCAb).
Must not have previously participated in a study involving LY2603618
Must not have previously taken pemetrexed for cancer
Must not have a known allergy to LY2603618 or pemetrexed
Must not currently have an infection that may affect participant's ability to tolerate the therapy
Must not have a serious medical condition or disorder that would make it unsafe for you to participate in the study such as uncontrolled diabetes or chest pain due to heart disease
If taking certain medications called non-steroidal anti-inflammatory drugs (NSAIDS), such as ibuprofen, must be able to stop taking these medications according to certain guidelines