A Study of Abemaciclib (LY2835219) in Combination With Another Anti-cancer Drug in Participants With Lung Cancer (NSCLC)

Inclusion Criteria:

* For all Parts: The participant must have stage IV non-small cell lung cancer (NSCLC).
* For Part A (abemaciclib + pemetrexed): Non-squamous subtypes only. The participant must have received at least one but no more than three prior therapies for advanced/metastatic NSCLC.
* For Part B (abemaciclib + gemcitabine): Any subtype. The participant must have received at least one but not more than three prior therapies for advanced/metastatic NSCLC.
* For Part C (abemaciclib + ramucirumab): Any subtype. The participant must have received at least two but not more than three prior therapies for advanced/metastatic NSCLC.
* For Part D (abemaciclib + LY3023414): Any subtype. The participant must have received at least two, but not more than three prior therapies for advanced/metastatic NSCLC. The participant must not have received prior treatment with any phosphoinositide 3-kinase (PI3K) or mammalian target of rapamycin (mTOR) inhibitor.
* For Part E (abemaciclib + pembrolizumab): Any subtype. The participant must have received at least one but no more than three prior therapies for advanced/metastatic NSCLC.
* Have either measureable or nonmeasurable disease as defined by the Response Evaluation Criteria in Solid Tumors (RECIST v1.1).
* Have adequate organ function including:

  * Hematologic: Absolute neutrophil count (ANC) 1.5 x 109/liter (L), platelets 100 x 109/L, and hemoglobin 8 gram/deciliter (g/dL).
  * Hepatic: Bilirubin 1.5 times upper limits of normal (ULN), alanine aminotransferase (ALT) and aspartate transaminase (AST) 3.0 times ULN. For participants with tumor involvement of the liver, AST and ALT equaling ≤5.0 times ULN are acceptable. Alkaline phosphatase ≤5.0 times ULN for participants with tumor involvement of the bone is acceptable.
  * Renal: Serum creatinine 1.5 times ULN.
* Have a performance status ≤1 on the Eastern Cooperative Oncology Group (ECOG) scale.
* Have discontinued all previous therapies for cancer (including chemotherapy, radiotherapy, immunotherapy, and investigational therapy) for at least 21 days for myelosuppressive agents or 14 days for nonmyelosuppressive agents prior to receiving study drug, and recovered from the acute effects of therapy (treatment related toxicity resolved to baseline) except for residual alopecia.
* Male and female participants of reproductive potential must agree to use medically approved contraceptive precautions during the trial and 3 to 4 months (as appropriate) following last dose of study drug.
* Have an estimated life expectancy of ≥12 weeks.
* Are able to swallow oral medications.

Exclusion Criteria:

* Have a personal history of any of the following conditions: presyncope or syncope of either unexplained or cardiovascular etiology, ventricular arrhythmia (including but not limited to ventricular tachycardia and ventricular fibrillation), or sudden cardiac arrest. Exception: Participants with controlled atrial fibrillation for \>30 days prior to study treatment are eligible.
* Parts A, B, D and E: Have central nervous system (CNS) metastasis with development of associated neurological changes 14 days prior to receiving study drug.
* Have a history of any other cancer (except non-melanoma skin cancer or carcinoma in-situ of the cervix or breast), unless in complete remission with no therapy for a minimum of 3 years.
* Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 3 to 4 months after the last dose of trial treatment (as appropriate).
* Have active bacterial, fungal, and/or known viral infection (for example, human immunodeficiency virus \[HIV\] antibodies, hepatitis B surface antigen \[HBSAg\], or hepatitis C antibodies). Screening is not required for enrollment.
* Parts A, B, C, and E: Have QTc interval of \> 470 millisecond (msec) on screening electrocardiogram (ECG). Part D participants have QTc interval of \>450msec on screening ECG.

Additional Exclusion Criteria For Part C

* History or evidence of cardiovascular risk including any of the following:

  * History of acute coronary syndromes (including myocardial infarction and angina), coronary angioplasty, or stenting within 6 months prior to enrollment.
  * History or evidence of current ≥Class II congestive heart failure as defined by New York Heart Association.
  * Treatment refractory hypertension defined as a blood pressure of systolic \>140 millimeter of mercury (mmHg) and/or diastolic \>90 mmHg which cannot be controlled by antihypertensive therapy.
  * Participants with intracardiac defibrillators.
* History or evidence of CNS disease. Radiographic screening of all participants without history of CNS metastasis is required.
* Radiographically documented evidence of major vessel invasion or encasement by cancer.
* Uncontrolled thromboembolic or hemorrhagic disorders.
* Participants receiving daily treatment with aspirin \>325mg/day or other known inhibitors of platelet function.
* History of gross hemoptysis within 2 months of study entry.
* Evidence of nonhealing wounds, ulcers, or bone fractures within 28 days prior to study entry.
* Undergone major surgery within 28 days prior to first dose of study drug or have subcutaneous venous access device placement within 7 days prior to first dose.

Additional Exclusion Criteria For Part D

* Have insulin-dependent diabetes mellitus or a history of gestational diabetes mellitus.
* Participants with a type 2 diabetes mellitus are eligible if adequate control of blood glucose level is obtained by oral anti-diabetic agents as documented by hemoglobin A1c (HbA1c) \<7%.
* History or evidence of cardiovascular risk including any of the following -- History of acute coronary syndromes (including myocardial infarction and angina), coronary angioplasty, or stenting within 6 months prior to enrollment.

Additional Exclusion Criteria for Part E

* Received prior monoclonal antibody (mAb) within 4 weeks prior to study.
* Has active autoimmune disease that has required treatment in the past 2 years.
* Has history of interstitial lung disease or pneumonitis.