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
patient'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 patient'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