Trametinib and Pembrolizumab in Treating Patients With Recurrent Non-small Cell Lung Cancer That Is Metastatic, Unresectable, or Locally Advanced

Inclusion Criteria:

* Histologically or cytologically confirmed diagnosis of metastatic or unresectable, locally advanced, recurrent NSCLC that has been previously treated (subjects who have failed adjuvant or locally advanced therapy within 6 months are also eligible to participate in the study)
* The subject has biopsy accessible tumor and is willing to undergo biopsy prior to planned protocol treatment
* Confirmation of the presence or absence of EGFR mutations and ALK gene fusions prior to study enrollment in all subjects except for patients with histologies other than adenocarcinoma and NSCLC, not otherwise specified (NOS), as the frequency of these alterations is exceedingly rare in this histology. Subjects with known EGFR sensitizing mutational status or ALK fusion must have been treated and progressed on EGFR TKIs or ALK-directed therapy, or with tumors harboring EGFR T790M mutation to have received and progressed on therapy directed at the T790M mutation (e.g. osimertinib). Subjects with known ROS1 translocation must have been treated and progressed on ROS1-directed therapy
* Measurable disease according to RECIST 1.1 and irRECIST. At least one lesion of at least 1.0 cm in the long-axis diameter for a non-lymph node or at least 1.5 cm in the short-axis diameter for a lymph node which is serially measurable according to RECIST 1.1 and irRECIST using either computed tomography (CT) or magnetic resonance imaging (MRI). If there is only one target lesion and it is a non-lymph node, it should have a longest diameter of at least 1.5 cm
* Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1
* Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L or at least 1500/mm\^3 or at least 1.5 x 10\^9/L
* Platelet count at least 100,000/mm\^3 or at least 100 x 10\^9/L
* Hemoglobin (Hb) at least 9 g/dL (or 5.69 mmol/L) at baseline (blood transfusions, hematopoietic growth factors and hematinics are not allowed during the 7 days prior to screening to correct Hb values less than 9 g/dL)
* Serum creatinine =\< 1.5 x upper limit of normal (ULN) or \>= 60 mL/minute for subjects with creatinine levels \> 1.5 x the institutional ULN
* Serum total bilirubin =\< 1.5 x ULN or direct bilirubin =\< ULN for subjects with total bilirubin levels \> 1.5 x ULN
* Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2.5 x ULN except for subjects with liver metastases (mets) for whom ALT and AST should be =\< 5 x ULN
* International normalized ratio (INR) or prothrombin time (PT) =\< 1.5 x ULN unless subject is receiving anticoagulant therapy as long as PT or partial thromboplastin time (PTT) is within therapeutic range of intended use of anticoagulants
* Activated PTT (aPTT) =\< 1.5 x ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulant
* Female subject of childbearing potential should have a negative urine or serum pregnancy 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 and male 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
* Voluntary agreement to provide written informed consent and the willingness and ability to comply with all aspects of the protocol
* Patients must be able to swallow and retain oral medication and must not have any clinically significant gastrointestinal abnormalities that may alter absorption such as malabsorption syndrome or major resection of the stomach or bowels
* Prior MEK inhibitor therapy is allowed
* Prior anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CD137, or anti-cytotoxic T-lymphocyte-associated antigen-4 (CTLA-4) antibody (including ipilimumab or any other antibody or drug specifically targeting T-cell co-stimulation or checkpoint pathways) is required for phase 2 part of the study. Subjects must be resistant (at least stable disease at 12 weeks of treatment with anti-PD1, anti-PD-L1 therapy) (cohort A) or refractory (progression within 12 weeks of starting anti-PD1 therapy) (cohort B) to an Food and Drug Administration (FDA) approved anti PD 1/PD L1 monoclonal antibody (mAb) as either monotherapy or in combination with other approved checkpoint inhibitors or other therapies according to their label, defined as (subjects must meet all of the following criteria):

  * Have received at least 2 doses of anti PD 1/PD L1 mAb
  * Progressive disease after anti PD 1/PD L1 mAb defined according to RECIST 1.1
  * Have documented progressive disease (PD) within 12 weeks of the last dose of anti PD 1/PD L1 mAb. Patients who were re-treated with anti PD 1/PD L1 mAb and patients who were on maintenance with anti PD 1/PD L1 mAb will be allowed to enter the trial as long as there is documented PD within 12 weeks of the last treatment date (with anti PD 1/PD L1 mAb)

    * Note - Subjects who have withdrawn from standard treatment due to unacceptable toxicity warranting discontinuation of that treatment and precluding retreatment with the same agent before progression of disease will also be eligible

Exclusion Criteria:

* Subjects participating in or who have participated in a study of an investigational agent or is using an investigational device within 4 weeks of the first dose of study treatment or have received any anti-cancer therapy, platinum-based chemotherapy, targeted, biological (including humanized antibodies), investigational, immunotherapy, or hormonal agent, within 4 weeks of the first dose of study 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
* Has had prior monoclonal antibody therapy within 4 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events (AEs) due to agents administered more than 4 weeks earlier
* Has received previous treatment with an immunomodulatory therapy (eg, anti PD 1/PD L1 or CTLA-4 agent) and was discontinued from that therapy due to a grade 3 or higher immune-related adverse event (irAE)
* Had prior chemotherapy, targeted small molecule therapy within 4 weeks, or radiation therapy within 2 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from AEs due to a previously administered agent

  * Note: subjects with =\< grade 2 neuropathy are an exception to this criterion and may qualify for the study
  * Note: if a subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy
  * Note: patients who have received \> 30 Gy to the thorax must have completed this radiation 6 months prior to enrollment in the study
* Has a known additional malignancy that is progressing or requires active treatment. Exceptions include basal cell and squamous cell carcinoma of the skin, or in situ cervical cancer that has undergone potentially curative therapy
* 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 4 weeks prior to the first dose of study 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 study treatment
* 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 evidence of interstitial lung disease or active, non-infectious pneumonitis, or has history of pneumonitis that required systemic corticosteroids for recovery
* Has an active infection requiring systemic therapy
* Has symptomatic ascites or pleural effusion. A subject who is clinically stable following treatment for these conditions (including therapeutic thoraco- or paracentesis) is eligible
* 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 study, or in the opinion of the investigator, is not in the best interest of the subject to participate
* Has known psychiatric or substance abuse disorders that could interfere with cooperation with the requirements of the protocol
* Is pregnant or breastfeeding, or expecting to become pregnant or father a child within the projected duration of the study, starting with the pre-screening or screening visit through 120 days after the last dose of study drug
* Has a known history of human immunodeficiency virus (HIV) (HIV ½ antibodies)
* Has known active hepatitis B (e.g., hepatitis B surface antigen \[HBsAg\] reactive) or hepatitis C (e.g., hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] \[qualitative\]) is detected
* Has received a live vaccine within 30 days prior to the first dose of study drug
* History or current evidence/risk of retinal vein occlusion (RVO)
* Patients who are currently receiving treatment with any medications that have the potential to prolong the QT interval if that treatment cannot be either discontinued or switched to a different medication (not known to affect QT interval) prior to cycle 1 day 1 (C1D1)
* Any of the following cardiac abnormalities or history: a) clinically significant abnormal 12-lead electrocardiogram (ECG), QT interval (QT corrected by Bazett's formula \[QTCB\]) \> 480 ms, b) inability to measure QT interval on ECG, c) personal or family history of long QT syndrome, d) implantable pacemaker or implantable cardioverter defibrillator, e) resting bradycardia \< 55 beats/min, f) history or evidence of current clinically significant uncontrolled arrhythmias. Exception: subjects with controlled atrial fibrillation for \> 30 days prior to randomization are eligible, g) history of acute coronary syndromes (including myocardial infarction and unstable angina), coronary angioplasty, or stenting, within 6 months prior to randomization, h) history or evidence of current \>= class II congestive heart failure as defined by New York Heart Association (NYHA), i) treatment refractory hypertension defined as a blood pressure of systolic \> 140 mm Hg and/or diastolic \> 90 mm Hg which cannot be controlled by antihypertensive therapy, j) cardiac metastases