Study of Palbociclib in Combination With Binimetinib for Patients With Advanced KRAS Mutant Non-Small Cell Lung Cancer

Inclusion Criteria: * Participants must have histologically confirmed advanced NSCLC (with a confirmed KRAS mutation via any CLIA-certified method) for which curable treatment modalities are not an option * Part I Dose Escalation: Participants are required to have measurable disease per RECIST 1.1 within 4 weeks of study entry * MTD Expansion and Part II: Participants must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \> 20 mm with conventional techniques or as \> 10 mm with spiral CT scan. See section 10 for the evaluation of measureable disease. * Age ≥ 18 years. Because no dosing or adverse event data are currently available in participants \< 18 years of age, children are excluded from this study * Participants are permitted to have any number of prior therapies prior to enrollment * ECOG performance status \< 2 (see Appendix A). * Participants must have normal organ and marrow function as defined below: * Absolute neutrophil count \> 1,500mm3 * Hemoglobin \> 9 g/dL * Platelets \> 100,000/mcL * Total bilirubin \< 2 X institutional upper limit of normal (ULN) * AST (SGOT)/ALT (SGPT) \< 2.5 X ULN -OR- * AST (SGOT)/ALT (SGPT) \< 5.0 X ULN if hepatic metastases are present * Creatinine \< 1.5 X the institutional ULN -OR- * Calculated creatinine clearance (determined as per Cockcroft-Gault) \> 50 mL/min * The effects of palbociclib and binimetinib on the developing human fetus are not fully known. For this reason, women of child-bearing potential and men must agree to use adequate contraception (combination hormonal and barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 90 days after discontinuation. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately. * Ability to understand and the willingness to sign a written informed consent document. * The availability of archival tissue to evaluate retrospectively the participant's Rb status. The requirement is a minimum of 5 unstained slides with each tissue cut measuring 4 microns in width. Ideally 15 slides will be requested. Patients without available archival tissue may be enrolled at the discretion of the principal investigator. * Patients must have recovered to ≤ Grade 1 in terms of toxicity from prior treatments (excluding neuropathy which can be ≤ Grade 2, and alopecia). * MTD Expansion: Patients must be willing to undergo pre- and on-treatment tumor biopsies. Patients are exempt from this requirement if, in the opinion of the investigator, the biopsy procedure would pose a significant risk or if they have only pulmonary metastatic disease. * Patients must be able to take oral medications. * Patients must have adequate cardiac function, defined as: * Left ventricular ejection fraction (LVEF) \> 50% as determined by echocardiogram or multigated acquisition scan (MUGA). * QTc \< 480 msec. Exclusion Criteria: * Participants who have had chemotherapy, radiotherapy, or major surgery within 2 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study. * Participants receiving any other study agents concurrently with the study drugs. * Participants with symptomatic brain metastases that require chronic steroids. Patients with a history of brain metastases are permitted to enroll as long as they have been treated, are off of steroids, and have been stable for a minimum of one month on imaging. * MTD Expansion: Patients currently taking anticoagulants and who cannot safely hold the medication to facilitate pre and on-treatment tumor biopsies are excluded from participation. * Concurrent use of strong CYP3A4 inhibitors/inducers is prohibited due to drug-drug interactions with palbociclib. Moderate CYP3A4 inhibitors/inducers should be used with caution (see Appendix C). * Part I Dose Escalation: Concurrent use of proton-pump inhibitors (PPIs) is prohibited. * Uncontrolled intercurrent illness including, but not limited to: * ongoing or active infection requiring systemic treatment * symptomatic congestive heart failure * cardiac arrhythmia * psychiatric illness/social situations that would limit compliance with study requirements * hypertension, defined as systolic blood pressure \> 160 mmHg despite medical management * myocardial infarction, unstable angina, coronary artery bypass grafting, coronary angioplasty, or stenting \< 6 months prior to screening * History of QT syndrome, Brugada syndrome, known history of QTc prolongation, or Torsades de Pointes. * History of Gilbert's syndrome. * History of neuromuscular disorders that are associated with elevated CK (e.g. inflammatory myopathies, muscular dystrophy, amyotrophic lateral sclerosis, spinal muscular atrophy). * History of other malignancy which could affect compliance with the protocol or interpretation of results. History of curatively treated basal or squamous cell carcinoma of the skin or in situ carcinoma of the cervix are allowed. Subjects with a malignancy that has been treated with curative intent will also be allowed if the malignancy has been in remission without treatment for ≥ 2 years prior to Cycle 1, Day 1. Subjects with localized prostate cancer that has been treated with curative intent will be allowed * Patients planning to embark on a new strenuous exercise regimen after the first dose of study treatment. * History of a malabsorption syndrome or uncontrolled nausea, vomiting, or diarrhea that may interfere with the absorption of oral study medication in the opinion of the investigator. * Pregnant women are excluded from this study because the study agents have the potential for teratogenic or abortifacient effects. As there is an unknown but potential risk of adverse events in nursing infants secondary to treatment of the mother with the study agents, breastfeeding must be discontinued if the mother is treated. * Part II: Individuals with a history of a different malignancy are ineligible except for the following circumstances: * They have been disease-free for at least 3 years and are deemed by the investigator to be at low risk for recurrence of that malignancy. * Individuals with the following cancers are eligible if diagnosed and curatively treated within the past 5 years: cervical cancer in situ, and basal or squamous cell carcinoma of the skin. * Known HIV-positive individuals on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions. Appropriate studies will be undertaken in participants receiving combination antiretroviral therapy when indicated. * Patients with known active hepatitis B and/or active hepatitis C infection. * Evidence of visible retinal pathology on screening ophthalmologic examination that places the participant at an unacceptable risk for retinal vein occlusion (e.g. uncontrolled glaucoma or ocular hypertension, history of hyperviscosity, etc.). * History of retinal degenerative disease. * Presence of neurosensory retinal detachment, retinal vein occlusion (RVO), or neovascular macular degeneration on screening ophthalmologic exam.