Trametinib and Docetaxel in Treating Patients With Recurrent or Stage IV KRAS Mutation Positive Non-small Cell Lung Cancer

Inclusion Criteria: * DISEASE RELATED CRITERIA: Patients must have pathologically confirmed KRAS mutation (at codon 12, 13 and 61) positive non-small cell lung cancer (NSCLC) that is stage IV or recurrent; the specific subtype of KRAS mutation must be known; KRAS mutation testing must have been performed in a Clinical Laboratory Improvement Act (CLIA) certified laboratory; CLIA certified commercially available tests are acceptable * DISEASE RELATED CRITERIA: Patients must have measurable disease documented by computed tomography (CT) or magnetic resonance imaging (MRI) within 28 days prior to registration; the CT from a combined positron emission tomography (PET)/CT may be used only if it is of diagnostic quality; non-measurable disease must be assessed within 42 days prior to registration; all known sites of disease must be assessed and documented on the baseline tumor assessment form (Response Evaluation Criteria in Solid Tumors \[RECIST 1.1\]) * DISEASE RELATED CRITERIA: Patients must not have known brain metastases, leptomeningeal carcinomatosis or spinal cord compression unless: (1) metastases have been locally treated (including stereotactic body radiation therapy \[SBRT\], whole brain radiotherapy \[WBRT\], and surgical resection) and have remained clinically controlled and asymptomatic for at least 14 days following treatment and prior to registration, AND (2) patient has no residual neurological dysfunction and has been off corticosteroids for at least 2 days prior to registration * PRIOR/CONCURRENT THERAPY CRITERIA: Patients must have documented progressive cancer following at least one but no more than two prior regimens of systemic therapy for lung cancer, one of which must have been platinum based combination chemotherapy; treatment with an immune therapy or targeted therapy for advanced disease will be considered a separate regimen and will count toward the prior regimens; maintenance therapy will not be counted as a separate regimen; adjuvant chemotherapy or chemotherapy administered as part of concurrent chemotherapy and radiation therapy for the treatment of lung cancer will not count as a prior regimen of systemic therapy as long as recurrence of patient's lung cancer occurred more than 12 months after the last day of chemotherapy * PRIOR/CONCURRENT THERAPY CRITERIA: Patients must not have received any chemotherapy, biologic agent, or any investigational agent within 14 days prior to registration. Patients must have recovered from any adverse events to Common Terminology Criteria for Adverse Events (CTCAE) grade 0-1 prior to registration * PRIOR/CONCURRENT THERAPY CRITERIA: Prior treatment with an anti-PD-1 or anti-PDL1 is not required * PRIOR/CONCURRENT THERAPY CRITERIA: Patients must not have received prior docetaxel; patients must not have received therapy with a drug known to be either a mitogen-activated protein kinase (MEK) inhibitor or a phosphatidylinositol 3 kinase (PI3K)/v-akt murine thymoma viral oncogene homolog 1 (AKT)/mammalian target of rapamycin (mTOR) pathway inhibitor * PRIOR/CONCURRENT THERAPY CRITERIA: Patients must have recovered from any adverse effects from prior therapy (except alopecia) to =\< CTCAE grade 1 prior to registration * PRIOR/CONCURRENT THERAPY CRITERIA: Patients may have had prior radiation therapy as long as it has not affected greater than 25% of the bone marrow and at least one measurable lesion is outside the area of prior radiation; at least 7 days must have elapsed since last radiation treatment; patients must have recovered from any adverse events from prior radiation therapy to =\< CTCAE grade 1 * PRIOR/CONCURRENT THERAPY CRITERIA: Patients must not have had a major surgery within 28 days prior to registration; patients must have recovered from any adverse effects of prior surgery to the satisfaction of the treating physician; biopsies and central IV access placement are not considered major surgery * PRIOR/CONCURRENT THERAPY CRITERIA: Because the composition, pharmacokinetics (PK), and metabolism of many herbal supplements are unknown, the concurrent use of all herbal supplements is prohibited during the study (including but not limited to St. John's wort, kava, ephedra \[ma huang\], ginko biloba, dehydroepiandrosterone \[DHEA\], yohimbe, saw palmetto, or ginseng) * CLINICAL/LABORATORY CRITERIA: Patients must have Zubrod performance status of 0-2 * CLINICAL/LABORATORY CRITERIA: Absolute neutrophil count (ANC) \>= 1500/mcL; these results must be obtained within 28 days prior to registration * CLINICAL/LABORATORY CRITERIA: Platelet count \>= 100,000/mcL; these results must be obtained within 28 days prior to registration * CLINICAL/LABORATORY CRITERIA: Hemoglobin \>= 9 grams/dl; these results must be obtained within 28 days prior to registration * CLINICAL/LABORATORY CRITERIA: Total bilirubin =\< 1.5 x institutional upper limit of normal (IULN); these results must be obtained within 28 days prior to registration * CLINICAL/LABORATORY CRITERIA: Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 x IULN (or =\< 5 x IULN for patients with known liver metastases); these results must be obtained within 28 days prior to registration * CLINICAL/LABORATORY CRITERIA: Serum creatinine =\< 1.5 x IULN OR measured or calculated creatinine clearance \>= 40 mL/min; this result must have been obtained within 28 days prior to registration * CLINICAL/LABORATORY CRITERIA: Patients must be able to swallow oral medications and must not have a gastro-intestinal disorder with diarrhea as a major symptom or that may alter absorption such as malabsorption syndromes or gastric resection * CLINICAL/LABORATORY CRITERIA: Patient must not have prior history of interstitial lung disease or pneumonitis * CLINICAL/LABORATORY CRITERIA: Patients must not have history of significant co-morbid illness inclusive of but not restricted to New York Heart Association class II, congestive cardiac failure, uncontrolled hypertension, history of myocardial infarction, unstable angina, coronary angioplasty, stenting or cerebrovascular accident within 6 months prior to registration or any other illness that in the assessment of the treating physician would compromise the ability of the patient to participate in this study * CLINICAL/LABORATORY CRITERIA: Patients must have corrected QT (QTc) interval =\< 480 msec (using the Bazett's formula) on electrocardiogram (ECG) performed within 42 days prior to registration; history or evidence of current clinically significant uncontrolled arrhythmias are not eligible; however, patients with controlled atrial fibrillation for \> 30 days prior to randomization are eligible; patients must not have atrial fibrillation \> grade 2 on the screening ECG; patients with CTCAE grade 1-2 atrial fibrillation on their screening ECG must have a second ECG performed prior to registration and more than 30 days from the screening ECG (either before or after) with the most recent ECG showing stable or improving grade of atrial fibrillation * CLINICAL/LABORATORY CRITERIA: Patients must have a left ventricular ejection fraction (LVEF) \>= institutional lower limit of normal (ILLN) by echocardiography (ECHO) or multi-gated acquisition scan (MUGA) within 42 days prior to registration * CLINICAL/LABORATORY CRITERIA: Patients must not have untreated or unresolved retinopathy or have a history (or current evidence) of retinal vein occlusion determined by an ophthalmology exam within 42 days prior to registration * CLINICAL/LABORATORY CRITERIA: Patients must not have an immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to trametinib, or excipients, or to dimethyl sulfoxide (DMSO) or other agents used in the study * CLINICAL/LABORATORY CRITERIA: Patients must not have a known history of active hepatitis B or C infection (defined as presence of hepatitis \[Hep\] B surface antigen \[sAg\] and/or Hep B deoxyribonucleic acid \[DNA\] and/or Hep C ribonucleic acid \[RNA\]); patients must not have a known history of human immunodeficiency virus (HIV) seropositivity * CLINICAL/LABORATORY CRITERIA: No other prior malignancy is allowed except for the following: adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, adequately treated stage I or II cancer from which the patient is currently in complete remission, or any other cancer from which the patient has been disease free for three years; patients with localized prostate cancer who are being followed by an active surveillance program are also eligible * CLINICAL/LABORATORY CRITERIA: Patients must not be pregnant or nursing due to the risk of fetal or nursing infant harm; women/men of reproductive potential must have agreed to use an effective contraceptive method (hormonal or barrier method of birth control; abstinence) prior to study entry, during the study participation and for 4 months after the last dose of the drug; a woman is considered to be of "reproductive potential" if she has had menses at any time in the preceding 12 consecutive months; in addition to routine contraceptive methods, "effective contraception" also includes heterosexual celibacy and surgery intended to prevent pregnancy (or with a side-effect of pregnancy prevention) defined as a hysterectomy, bilateral oophorectomy or bilateral tubal ligation; however, if at any point a previously celibate patient chooses to become heterosexually active during the time period for use of contraceptive measures outlined in the protocol, he/she is responsible for beginning contraceptive measures * SPECIMEN SUBMISSION CRITERIA: Patients must be offered optional participation in banking of specimens for future research * REGULATORY CRITERIA: Patients must be informed of the investigational nature of this study and must sign and give written informed consent in accordance with institutional and federal guidelines * REGULATORY CRITERIA: As a part of the Oncology Patient Enrollment Network (OPEN) registration process the treating institution's identity is provided in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered in the system