Pembrolizumab and Trametinib in Treating Patients With Stage IV Non-Small Cell Lung Cancer and KRAS Gene Mutations

Inclusion Criteria: * Stage IV or metastatic/recurrent non-small cell lung cancer; for expansion cohorts, patient's tumor must also harbor a KRAS mutation detected in a CLIA certified laboratory * Have histologically or cytologically confirmed non-small cell lung cancer * Have stage IV, metastatic or recurrent non-squamous non-small cell lung cancer (NSCLC) with progressive disease after platinum containing chemotherapy (EGFR mutant, ALK, or ROS-1 rearranged NSCLC must have progressed on prior approved tyrosine kinase inhibitor \[TKI\]'s) * For phase I dose expansion cohorts the patient's tumor must harbor a KRAS mutation detected by a CLIA certified laboratory * Be willing and able to provide written informed consent/assent for the trial * Have measurable disease based on Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 * Be willing to provide tissue from a newly obtained core or excisional biopsy of a tumor lesion; in the opinion of the investigator, the patient must have tumor accessible by CT or ultrasound guided core biopsy; subjects for whom newly-obtained samples cannot be provided may submit an archived specimen provided it was obtained after last systemic treatment, within 6 months of signing consent and that tissue is available for either 2 cell blocks or 20 uncut slides (core or excisional biopsy required, fine needle aspirate is not acceptable) * Have a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) Performance Scale * Able to swallow and retain orally administered medication and does not have any clinically significant gastrointestinal abnormalities that may alter absorption such as malabsorption syndrome or major resection of the stomach or bowels * Absolute neutrophil count \>= 1.5 x 10\^9/L * Hemoglobin \>= 9 g/dL * Platelets \>= 100 x 10\^9/L * Prothrombin time (PT)/international normalized ratio (INR) and partial thromboplastin time (PTT) =\< 1.5 x upper limit of normal (ULN) * Albumin \>= 2.5 g/dL * Total bilirubin =\< 1.5 x ULN * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 x ULN * Creatinine =\< 1.5 ULN * Calculated creatinine clearance \>= 50 mL/min * Left ventricular ejection fraction (LVEF) \>= lower limit of normal (LLN) by echocardiogram (ECHO) or multigated acquisition (MUGA) * Female subject of childbearing potential should have a negative urine or serum pregnancy test within 72 hours prior to receiving the first dose of study medication; if the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Female subjects of childbearing potential must be willing to use an adequate method of contraception for the course of the study through 120 days after the last dose of study medication; note: abstinence is acceptable if this is the usual lifestyle and preferred contraception for the subject * Male subjects of childbearing potential must agree to use an adequate method of contraception starting with the first dose of study therapy through 120 days after the last dose of study therapy; note: abstinence is acceptable if this is the usual lifestyle and preferred contraception for the subject * Clarification: subjects with atrial fibrillation controlled for \> 30 days prior to dosing are eligible Exclusion Criteria: * Is currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy or used an investigational device within 3 weeks of the first dose of treatment * Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment; inhaled or topical steroids are allowed * Has a known history of active tuberculosis (TB \[Bacillus Tuberculosis\]) * Hypersensitivity to pembrolizumab or any of its excipients * Has had a prior anti-cancer monoclonal antibody (mAb) within 3 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to agents administered more than 3 weeks earlier * Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to a previously administered agent; note: subjects with =\< grade 2 neuropathy or alopecia are an exception to this criterion and may qualify for the study; note: if subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy * Has a known additional malignancy that is progressing or requires active treatment; exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer * Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis; subjects with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least four weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 7 days prior to trial treatment; this exception does not include carcinomatous meningitis which is excluded regardless of clinical stability * Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs); replacement therapy (eg., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment * Has known history of, or any evidence of active, non-infectious pneumonitis; history of radiation pneumonitis is allowed provided that it is not active and no corticosteroids were required for pneumonitis management * Evidence of interstitial lung disease * Has an active infection requiring systemic therapy * Have a known immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to trametinib, or excipients or to dimethyl sulfoxide (DMSO) * History of retinal vein occlusion (RVO) * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial * 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 120 days after the last dose of trial treatment * Has received prior therapy with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent for dose expansion; (patients in dose escalation may have received an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent) * Has a known history of Human Immunodeficiency Virus (HIV) (HIV 1/2 antibodies) * Has known active Hepatitis B (e.g., hepatitis B virus surface antigen \[HBsAg\] reactive) or Hepatitis C (e.g., hepatitis C virus (HCV) ribonucleic acid (RNA) \[qualitative\] is detected) * LVEF \< LLN on screening exam * A QT interval corrected for heart rate using the Fridericia's formula (QTcF) \>= 470 msec on screening exam * History or evidence of current clinically significant uncontrolled arrhythmias * History of acute coronary syndromes (including myocardial infarction and unstable 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 (NYHA) * Treatment refractory hypertension defined as a blood pressure of systolic \> 140 mmHg and/or diastolic \> 90 mm Hg which cannot be controlled by anti-hypertensive therapy * Patients with intra-cardiac defibrillators * Has received a live vaccine within 30 days of planned start of study therapy; note: seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist) are live attenuated vaccines, and are not allowed