Osimertinib and Tegavivint as First-Line Therapy for the Treatment of Metastatic EGFR-Mutant Non-small Cell Lung Cancer

Inclusion Criteria: * Age \>= 18 years. Children are excluded from this study because neither dosing nor safety data are currently available for AZD9291 or BC2059 in patients \< 18 years of age * Pathology-confirmed metastatic NSCLC * A common activating mutation must be present in the EGFR gene, i.e., exon 19 deletion or L858R. The presence of uncommon EGFR mutations, e.g., G719X, S768I, or L861Q are also permitted if they co-occur with a common activating mutation. Mutation status must be determined using a tumor biopsy by local Clinical Laboratory Improvement Act (CLIA)-certified assessment. Mutations identified by blood-based testing can be provided, but must be verified by tumor biopsy * The presence of a concurrent T790M mutation, while uncommon in patients who are naïve to treatment with EGFR TKIs, is also permitted * Measurable disease as defined by Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1 criteria * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * The patient must be able to swallow pills * Life expectancy \> 3 months * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Hemoglobin \>= 90 g/L * Total bilirubin =\< 1.5 x institutional upper limit normal (ULN) and up to 3 mg/dL for patients with Gilbert's * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase ALT (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional ULN and =\< 5 x institutional ULN for patients with liver metastases * Creatinine within 1.5 x ULN OR glomerular filtration rate (GFR) \>= 50 mL/min/1.73 m\^2 (measured or calculated by Cockcroft and Gault equation) -confirmation of creatinine clearance is only required for patients with creatinine levels above institutional upper limit of normal * If evidence of chronic hepatitis B virus (HBV) infection, HBV viral load must be undetectable on suppressive therapy if indicated * If history of hepatitis C virus (HCV) infection, it must be treated and have an undetectable viral load * Patients with treated brain metastases are asymptomatic and not requiring ongoing treatment * Patients with new or progressive brain metastases (active brain metastases) or leptomeningeal disease are eligible if the treating physician determines that immediate central nervous system (CNS)-specific treatment is not required and is unlikely to be required during the first cycle of therapy. Clinical stability on a stable dose of decadron is permitted * Patients with a prior or concurrent malignancy whose natural history or treatment will not interfere with the safety or efficacy assessment of the investigational drugs are eligible for this trial * Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients must be class 2B or better * Ability to understand and sign a written informed consent document Exclusion Criteria: * Prior treatment with an EGFR TKI in any setting * Patients who have not recovered from adverse events (AEs) due to prior anti-cancer therapy (i.e., have residual toxicities \> grade 1), with the exception of alopecia * Past medical history of interstitial lung disease, drug-induced interstitial lung disease, radiation pneumonitis requiring steroid treatment, or any evidence of clinically active interstitial lung disease * Patients who are receiving any other investigational agent or immunotherapy within five half-lives of the compound or 3 months, whichever is greater * Patients with an uncontrolled intercurrent illness * Patients with psychiatric illness/social situations that would limit compliance with study requirements * History of allergic reactions attributed to compounds of similar chemical or biologic composition as BC2059 or AZD9291. Patients with hypersensitivity to any of the inactive excipients should also be excluded * Currently receiving (or unable to stop use prior to receiving the first dose of study treatment) medications or herbal supplements known to be potent inducers of CYP3A4 (wash-out periods vary. All patients must try to avoid concomitant use of any medications, herbal supplements and/or ingestion of foods with known inducer effects on CYP3A4 * Pregnant women are excluded from this study because BC2059 has the potential for teratogenic or abortifacient effects. There is also an unknown but potential risk for AEs in nursing infants secondary to treatment of the mother with AZD9291 or BC2059. Breastfeeding patients will be excluded * Patients with a significant history of cardiovascular disease (e.g., myocardial infarction \[MI\], thrombotic or thromboembolic event in the last 6 months) * Any of the following cardiac criteria: * Mean resting corrected QT interval (corrected QT \[QTc\] using Fredericia's formula \[QTcF\]) \> 470 msec. RR is the time from the interval of 1 QRS complex to the next measured in seconds and is commonly calculated as (60/HR) * Any clinically important abnormalities in rhythm, conduction or morphology of resting ECG (e.g., complete left bundle branch block, third degree heart block, second degree heart block) * Any factors that increase the risk of QTc prolongation or risk of arrhythmic events such as decompensated heart failure, hypokalemia, congenital long QT syndrome, family history of long QT syndrome or unexplained sudden death under 40 years of age in first degree relatives, or any concomitant medication known to prolong the QT interval * Left ventricular ejection fraction (LVEF) \< lower limit of normal (LLN) as assessed by either multigated acquisition (MUGA) scan or echocardiogram (ECHO) * Patients with active malignancies other than NSCLC or patients with prior curatively treated malignancy at high risk of relapse during the study period with the exception of localized squamous or basal cell skin cancers, ductal carcinoma in-situ (DCIS), or indolent cancer currently on observation (i.e. chronic lymphocytic leukemia \[CLL\] or low-risk prostate cancer) * Any evidence of severe or uncontrolled systemic disease, including uncontrolled hypertension and active bleeding diatheses, which in the investigator's opinion makes it undesirable for the patient to participate in the trial or which would jeopardize compliance with the protocol, or active infection with human immunodeficiency virus (HIV). Screening for chronic conditions is not required * Patients who are at risk for impaired absorption of oral medication including, but not limited to, refractory nausea and vomiting, chronic gastrointestinal diseases, inability to swallow the formulated product or previous significant bowel resection that would preclude adequate absorption of AZD9291 * Judgment by the investigator that the patient should not participate in the study if the patient is unlikely to comply with study procedures, restrictions, or requirements * Involvement in the planning and/or conduct of the study (applies to both investigator staff and/or staff at the study site)