Trial of Trametinib and Ponatinib in Patients With KRAS Mutant Advanced Non-Small Cell Lung Cancer

Inclusion Criteria: * Histologically or cytologically proven diagnosis of advanced lung adenocarcinoma * KRAS mutation * Radiographic progression following prior treatment with platinum doublet chemotherapy and prior treatment with a PD-1/L1 inhibitor. Patients who are deemed not eligible for therapy with a PD-1/L1 inhibitor by their treating physician will also be eligible. * Able to take oral medications * Measurable disease as per RECIST 1.1. Previously irradiated sites of tumor may be considered measurable if there is radiographic progression at the site subsequent to the time of completing radiation. * Karnofsky performance status (KPS) ≥ 70% * Age \>18 years old * Adequate organ function: * AST, ALT ≤ 2.5 x ULN - Total bilirubin ≤ 1.5 x ULN -Albumin ≥ 2.5g/dL * Creatinine \< 1.5 x ULN OR calculated creatinine clearance ≥ 50mL/min * Absolute neutrophil count (ANC) ≥ 1,200 cells/mm\^3 * Hemoglobin ≥ 9.0 g/dL * Platelets ≥ 100,000/mm\^3 * Amylase and lipase within normal limits (amylase ≤ 100, lipase ≤ 78) * Female patients who: * Are postmenopausal for at least 1 year before the screening visit, OR * Are surgically sterile, OR * If they are of childbearing potential, agree to practice 2 effective methods of contraception, at the same time, from the time of signing the informed consent through 30 days after the last dose of study drug, or agree to completely abstain from heterosexual intercourse * Male patients, even if surgically sterilized (i.e., status post-vasectomy), who: * Agree to practice effective barrier contraception during the entire study treatment period and through 30 days after the last dose of study drug, or * Agree to completely abstain from heterosexual intercourse Exclusion Criteria: * Patients with symptomatic brain metastasis requiring escalating doses of steroids * Patients with grade 2 or greater diarrhea prior to study initiation despite maximal medical management * History of acute pancreatitis within 1 year of study entry or history of chronic pancreatitis * History of or ongoing alcohol abuse that, in the opinion of the Investigator, would compromise compliance or impart excess risks associated with study participation. * Pregnant or lactating women * Any type of systemic therapy (chemotherapy or experimental drugs) within 2 weeks of starting treatment on protocol * Patients who have received prior treatment with MEK inhibitor * A history of clinically significant interstitial lung disease or pneumonitis * Significant uncontrolled or active cardiovascular disease, specifically including, but not restricted to: History of clinically significant (as determined by the treating physician) atrial arrhythmia; or any ventricular arrhythmia, History of congenital long QT syndrome., Abnormal QTc (≥ 450 msec in males and ≥ 470 msec in females), Ejection fraction ≤ 50% as assessed by echocardiogram. * History of arterial thrombotic disease, specifically including, but not restricted to: Myocardial infarction or unstable angina, cerebrovascular event (CVA) or transient ischemic attack (TIA), Peripheral vascular disease or claudication. * Uncontrolled hypertension (Diastolic blood pressure \> 100 mmHg; Systolic blood pressure \> 150 mmHg). * History of venous thromboembolism (e.g. deep venous thrombosis or pulmonary embolism) within 6 months of study entry. Note: Participants enrolled after this window must be on appropriate therapeutic anticoagulation. * History of central serous retinopathy or retinal vein occlusion * Patients with baseline risk factors for central serous retinopathy or retinal vein occlusion such as evidence of new optic disc cupping, evidence of new visual field defects, and intraocular pressure \>21 mmHg are excluded from the trial * History of prior malignancy within 2 years that requires treatment. Patients who are considered NED from a malignancy may be considered on a case by case basis. * Any other condition that, in the opinion of the investigator, may compromise the safety, compliance of the patient, or would preclude the patient from successful completion of the study