• Patients must have histologically confirmed metastatic non-small cell lung cancer (NSCLC) with activating EGFR mutation including typical and atypical mutations in egfr exons 19 and 21

• Eastern Cooperative Oncology Group (ECOG) performance status of 0-2

• Patients in the expansion cohort 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 (\>= 2 cm) by chest x-ray or as \>= 10 mm (\>= 1 cm) with computed tomography (CT) scan, magnetic resonance imaging (MRI), or calipers by clinical exam

• Ability to safely swallow oral medication

• Absolute neutrophil count \>= 1500/mm\^3

• Platelet count \>= 100,000/mm\^3

• Hemoglobin \>= 8.5 g/dL (must be \> 2 weeks post-red blood cell transfusion)

• Bilirubin =\< 1.5 x the upper limit of normal (ULN). For subjects with documented Gilbert's disease, bilirubin =\< 3.0 mg/dL. For subjects with documented liver metastases, bilirubin =\< 2.5 x ULN

• Serum creatinine =\< 1.5 x the ULN or creatinine clearance (CrCl) \>= 50 mL/min. For creatinine clearance estimation, the Cockcroft and Gault equation should be used

• Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 3 x the ULN (=\< 5 x the ULN for subjects with liver metastases)

• The effects of MRX-2843 and osimertinib 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 and for the duration of study participation. 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. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of study drug administration

• Females of childbearing potential who are sexually active with a non-sterilized male partner agree to use 2 methods of effective contraception from screening, and agree to continue using such precautions for 90 days after the final dose of study drug; cessation of birth control after this point should be discussed with a responsible physician. Females of childbearing potential are defined as those who are not surgically sterile (i.e., bilateral tubal ligation, bilateral oophorectomy, or complete hysterectomy) or postmenopausal (defined as 12 months with no menses without an alternative medical cause)

• Non-sterilized males who are sexually active with a female of childbearing potential must agree to use an acceptable method of effective contraception from Day 1 and for 90 days after the final dose of study drug

• Female subjects of childbearing potential must be nonpregnant, and have a negative pregnancy test result at screening and day 1 of cycles 1-6

• Ability to understand and the willingness to sign a written informed consent document

• COHORT SPECIFIC ELIGIBILITY REQUIREMENTS

• Dose Escalation Cohort: Patients with progressive EGFR (+) NSCLC disease; previously treated or naive to EGFR-tyrosine kinase inhibitor (TKI) (previous treatment with 3rd generation EGFR-TKI including osimertinib allowed

• Dose Expansion Cohort A (Treatment naive):

‣ Be treatment naive to osimertinib or any other EGFR TKI,

⁃ If treated with an EGFR TKI in the adjuvant, must have discontinued treatment prior to disease recurrence and be free of recurrence for at least 12 months (+1 day) while off treatment

• Dose Expansion Cohort B (EGFR TKI resistant):

‣ Have progression of disease on osimertinib, erlotinib, gefitinib or afatinib as last previous systemic treatment,

⁃ If not previously treated with osimertinib, must be EGFR-T790M negative as confirmed using a standard testing platform (circulating tumor deoxyribonucleic acid \[ctDNA\] or tissue based testing) prior to study treatment

• Backfill Cohort C: This cohort will be open to candidates who are not able to get into any of the dose escalation or expansion cohorts. Examples will be a patient already on osimertinib but without disease progression or an otherwise eligible patient who is unable to wait for new cohorts to open due to disease burden and symptoms.

∙ Such patients may be enrolled into the backfill cohort if they meet the following criteria:

• Patients must meet the general eligibility requirements but do not meet cohort specific requirements,

• If currently on osimertinib, must have tolerated the standard dose of 80 mg for at least 2 cycles without any grade \> 2 adverse events,

• Will be treated at a dose previously established to be safe from the dose escalation cohort,

• Will not be included in the dose limiting toxicity (DLT) or maximum tolerated dose (MTD) determination,

• Approval by the study sponsor