Inclusion Criteria:
* Patients must have been histologically or cytologically diagnosed with non-small cell lung cancer, specifically lung adenocarcinoma
* Patients must have advanced stage disease that is not amenable to combined modality therapy or surgical resection
* Patients must have known LKB1 mutation
* COHORT A ONLY: Patients must have known KRAS mutation
* Patients must have progressed on prior therapy with immune checkpoint inhibitor alone and first line chemotherapy, either combined or sequentially, for advanced stage disease. No other lines of chemotherapy in the advanced stage therapy is allowed. The exception is patients with KRAS G12C are also allowed the use of one line of targeted Food and Drug Administration (FDA) approved therapy
* Patients 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 for non-nodal lesions and short axis for nodal lesions) as ≥ 20 mm with conventional techniques or as ≥ 10 mm with spiral CT scan
* Age ≥ 18 years
* Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1
* Adequate recovery from toxicities related to prior treatments to at least grade 1 by Common Terminology Criteria for Adverse Events (CTCAE) version (v) 5.0. Exceptions include alopecia and peripheral neuropathy grade ≤ 2
* Absolute neutrophil count ≥ 1,500/mcL
* Hemoglobin ≥ 8.0
* Platelets ≥ 100,000/mcL
* Total bilirubin ≤ 1.5 x upper limit of normal (ULN) for the institution; patients with Gilbert syndrome may enroll if total bilirubin \< 3.0 mg/dL (51 umole/L)
* Aspartate aminotransferase (AST)(serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT)(serum glutamic pyruvic transaminase \[SGPT\]) alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 2.5 x ULN (or \< 5 x ULN in patients with liver metastases)
* Creatinine clearance ≥ 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal
* Patients must have the ability to ingest oral medications
* The effects of defactinib and avutometinib on the developing human fetus are unknown. For this reason, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry,for the duration of study participation, for 3 months following the last dose of study therapy for male patients, and 1 month following the last dose of study therapy for female patients. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately
* Patients must be able to understand and be willing to sign a written informed consent document
* Baseline corrected QT (QTc) interval \< 460 ms for women and ≤ 450 ms for men (average of triplicate readings) (CTCAE grade 1) using Fredericia's QT correction formula. NOTE: This criterion does not apply to patients with a right or left bundle branch block
Exclusion Criteria:
* Patients who have had systemic therapy within 3 weeks prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier
* Patients who are receiving any other investigational agents
* Patients with unstable or symptomatic brain metastasis or known leptomeningeal disease. Asymptomatic brain metastases are allowed if they meet the following criteria:
* Have been treated and have been stable for greater than or equal to 4 weeks as documented by radiologic imaging
* Have not required increasing doses of corticosteroids within 2 weeks prior to study treatment
* Patients with history of pre-existing auto-immune conditions that would pose a higher risk for toxicity with nivolumab will be excluded
* Patients who experienced serious auto-immune toxicity with prior immune checkpoint inhibitor therapy
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to avutometinib or defactinib
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
* Known hepatitis B, hepatitis C or human immunodeficiency virus (HIV) infection that is active and/or requires therapy
* Active skin disorder that has required systemic therapy within the past 1 year. Surgically removed early stage skin cancers are allowed. Topical creams are allowed as well
* History of rhabdomyolysis
* Concurrent ocular disorders:
* Patients with history of glaucoma, history of retinal vein occlusion (RVO), predisposing factors for RVO, including uncontrolled hypertension, uncontrolled diabetes
* Patients with history of retinal pathology or evidence of visible retinal pathology that is considered a risk factor for RVO, intraocular pressure \> 21 mm Hg as measured by tonometry, or other significant ocular pathology, such as anatomical abnormalities that increase the risk for RVO
* Patients with active or chronic, visually significant corneal disorders, other active ocular conditions requiring ongoing therapy or clinically significant corneal disease that prevents adequate monitoring of drug-induced keratopathy. Examples of visually significant corneal disorders include corneal degeneration, active or recurrent keratitis, and other forms of serious ocular surface inflammatory conditions. Visually significant corneal disorders do NOT include dry eyes, blepharitis, and uncomplicated corneal erosions
* Patients with the inability to swallow oral medications or impaired gastrointestinal absorption due to gastrectomy or active inflammatory bowel disease
* Treatment with warfarin. Patients on warfarin for deep vein thrombosis/pulmonary embolism should be converted to low-molecular-weight heparin (LMWH) or direct oral anticoagulants (DOACs). Exposure to medications (with or without prescriptions), supplements, herbal remedies, or foods with potential for drug-drug interactions with defactinib within 14 days prior to the first dose of avutometinib or defactinib and during the course of therapy, including:
* Strong CYP3A4 inhibitors or inducers, strong CYP2C9 inhibitors or inducers, strong P-glycoprotein (P-gp) inhibitors or inducers
* Patients with a known "treatable driver mutation" with FDA approved targeted therapy (such as EGFR, ALK, ROS1, NTRK, BRAF, RET, MET exon 14, HER2). The exception is KRAS as listed in the inclusion section
* History of prior malignancy within past 2 years prior to study entry, with the exception of curatively treated malignancies or malignancies with very low potential for recurrence or progression
* Female patients who are pregnant or breastfeeding
Active drug
