A Study of Necitumumab and Abemaciclib in Participants With Non-Small Cell Lung Cancer (NSCLC)

Inclusion Criteria: * Histologically or cytologically confirmed NSCLC Stage IV: * Part A: NSCLC Stage IV (any type). * Part B: NSCLC Stage IV (squamous and nonsquamous). * Measurable disease at the time of study entry as defined by Response Evaluation Criteria in Solid Tumors Version 1.1 (RECIST 1.1). * The participant must have progressed after platinum-based chemotherapy AND have received a maximum of 1 other prior chemotherapy for advanced and/or metastatic disease OR must be judged by the physician as ineligible for further standard second-line chemotherapy. Prior treatment with epidermal growth factor receptor-tyrosine kinase inhibitor (EGFR-TKI) and anaplastic lymphoma kinase (ALK) inhibitors is mandatory in participants whose tumor has EGFR-activating mutations or ALK translocations. Prior targeting agents and neoadjuvant/adjuvant therapies are permitted with the exception of cyclin-dependent kinase (CDK)4/6-targeting agents or necitumumab. * The participant has tumor tissue available for biomarker analyses. * The participant has an Eastern Cooperative Oncology Group performance status score of 0-1. * Have adequate organ functions. Exclusion Criteria: * The participant is currently enrolled in a clinical trial involving an investigational product or non-approved use of a drug or device. Prior treatment with cyclin-dependent kinase 4 and 6 (CDK4/6) - targeting agents or necitumumab is not permitted. * Have a serious concomitant systemic disorder or significant cardiac disease. * The participant has undergone major surgery or received any investigational therapy in the 30-days prior to study enrollment. * The participant has undergone chest irradiation within 4 weeks prior to receiving study treatment. * The participant has brain metastases that are symptomatic. * History of arterial or venous thromboembolism within 3 months prior to study enrollment. Participants with a history of venous thromboembolism beyond 3 months prior to study enrollment can be enrolled if they are appropriately treated with low molecular weight heparin. * The participant has active infection requiring systemic therapy. * The participant has a known allergy / history of hypersensitivity reaction to any of the treatment components, including any ingredient used in the formulation of necitumumab or abemaciclib, or any other contraindication to one of the administered treatments. * The participant is pregnant or breastfeeding. * The participant has a concurrent active malignancy. Previous history of malignancy is permitted, provided that the participant has been free of disease for ≥3 years, with the exception of adequately treated basal or squamous cell carcinoma of the skin, preinvasive carcinoma of the cervix, or any cancers that in the judgment of the investigator and sponsor may not affect the interpretation of results (for example, prostate, bladder). * History of interstitial lung disease or an active non-infectious pneumonitis.