Osimertinib and Necitumumab in Treating Patients With EGFR-Mutant Stage IV or Recurrent Non-small Cell Lung Cancer Who Have Progressed on a Previous EGFR Tyrosine Kinase Inhibitor

Patients with stage IV or recurrent/metastatic histologically confirmed non-small cell lung cancer (NSCLC)

NSCLC must harbor at least one of the following EGFR activating mutations: Exon 21 L858R, Exon 19 deletion, Exon 18 G719X, Exon 21 L861Q or for EGFR Exon 20 insertion expansion cohort D, NSCLC must harbor an EGFR Exon 20 insertion performed by a Clinical Laboratory Improvement Act (CLIA) certified test

For Dose escalation cohort - progressive disease on at least one prior EGFR-TKI (previous treatment with 3rd generation EGFR-TKI including osimertinib \[AZD9291\] allowed for dose escalation)

For Dose Expansion Cohort A: patient must 1) have progression of disease on erlotinib, gefitinib or afatinib as last previous systemic treatment, 2) have biopsy of tumor taken after progression on erlotinib, gefitinib or afatinib which must be EGFR-T790M negative confirmed by central testing prior to treatment (if EGFR-T790M status is unknown, patients may consent for trial and for biopsy and testing for EGFR T790M will be performed as part of initial biopsy for trial), and 3) be treatment naive to 3rd generation EGFR-TKI (rociletinib, EGFR inhibitor HM61713 \[HM61713\] and osimertinib \[AZD9291\]) and EGFR monoclonal antibodies

For Dose Expansion Cohort B (closed to accrual as of 8/30/18): patient must 1) have progression of disease on a 3rd generation EGFR-TKI such as AZD9291, rociletinib, HM61713, 2) be treatment naive to an EGFR monoclonal antibody, and 3) have a biopsy of tumor taken after progression on last EGFR-TKI that indicates loss of EGFR-T790M (EGFR-T790M negative) confirmed by central testing prior to treatment (if EGFR-T790M status is unknown, patients may consent for trial and for biopsy, and testing for EGFR T790M will be performed as part of initial biopsy for trial)

For Dose Expansion Cohort C: patient must 1) have progression of disease on a 3rd generation EGFR-TKI such as osimertinib (AZD9291), rociletinib, HM61713, 2) be treatment naive to an EGFR monoclonal antibody, 3) have a biopsy of tumor taken after progression on last EGFR-TKI that indicates preservation of EGFR-T790M post-progression on 3rd generation EGFR-TKI with biopsy confirmation by central testing prior to treatment (if EGFR-T790M status is unknown, patients may consent for trial and for biopsy, and testing for EGFR T790M will be performed as part of initial biopsy for trial)

For Dose Expansion Cohort D: patient must 1) tumor that harbors an EGFR Exon 20 insertion by a CLIA certified test, and 2) have progressive disease on or after platinum based chemotherapy, and 3) be treatment naïve to 3rd generation and beyond EGFR-TKI (i.e., osimertinib \[AZD9291\], poziotinib, TAK-778) and EGFR monoclonal antibody; patient who received 1st or 2nd generation EGFR-TKI (such as erlotinib, gefitinib, afatinib) are eligible provided that they did not achieve a response to treatment or they did not have a duration of treatment on EGFR-TKI of 6 months or more

For Dose Expansion Cohort E: patient must have progressive disease on osimertinib (AZD9291) as first-line EGFR-TKI treatment for metastatic NSCLC; patients must also be treatment naive to EGFR-monoclonal antibody

Adequate archival tissue from a biopsy performed after progression of disease on previous EGFR-TKI or willing to consent for a fresh tumor biopsy; (mandatory for Cohorts A, B, C; optional for dose escalation and Cohort D, and Cohort E)

Patients must have measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1, defined as at least one lesion that can be accurately measured in at least one dimension \>= 10 mm (\>= 1 cm) by computed tomography (CT) imaging or magnetic resonance imaging (MRI) within 42 days prior to registration; the CT from a combined positron emission tomography (PET)/CT may be used only if it is of diagnostic quality; laboratory parameters are not acceptable as the only evidence of disease

Any number of prior therapies is allowed

Age \>= 18 years. NSCLC is exceedingly rare in patients \< 18 years of age. Because no dosing or adverse event data are currently available on the use of and necitumumab in patients \< 18 years of age, children are excluded from this study

Eastern Cooperative Oncology Group (ECOG) performance status =\< 1

Patients must have the ability to swallow tablets

Life expectancy of greater 3 months

Absolute neutrophil count \>= 1,500/mcL

Platelets \>= 100,000/mcL

Total bilirubin =\< 1.5 x upper limit of normal (ULN) (patients with Gilbert's syndrome may have serum bilirubin \> 1.5 ULN)

Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3.0 x institutional upper limit of normal

Creatinine =\< 1.5 x ULN OR

Creatinine clearance \>= 50 mL/min

The effects of osimertinib (AZD9291) and necitumumab on the developing human fetus are unknown; for this reason, women of child-bearing potential and men must agree to use adequate contraception using one of the methods listed below prior to study entry, for the duration of study participation, and for 3 months for women and 6 months for men following the date of the last dose of osimertinib (AZD9291) and/or necitumumab:

* Total abstinence from sexual intercourse (minimum one complete menstrual cycle prior to study drug administration);

* Vasectomized male subject or vasectomized partner of female subjects

* Hormonal contraceptives (oral, parenteral, transdermal or vaginal ring) prior to study drug administration; if the subject is currently using a hormonal contraceptive, she should also use a barrier method during this study and for 3 months after study completion;

* Intrauterine device (IUD);

* Double-barrier method: male condom plus diaphragm or vaginal cap with spermicide (contraceptive sponge, jellies or creams)

* Additionally, for all methods above (except for abstinence), male subjects (including those who are vasectomized) whose partners are pregnant or might be pregnant must use condoms for the duration of the study and for 6 months following completion of therapy

Women of childbearing potential must have a negative urine pregnancy test within 7 days prior to initiation of treatment; women will be considered not of childbearing potential if they are surgically sterile (bilateral oophorectomy or hysterectomy) and/or post menopausal (amenorrheic for at least 12 months); 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 with untreated brain metastases are allowed provided that the patient is clinically asymptomatic and stable; patients with a prior history of symptomatic brain metastases are eligible provided:

* The brain metastases have been treated

* The patient is asymptomatic from the brain metastases at enrollment

* Corticosteroids prescribed for the management of brain metastases have been discontinued at least 7 days prior to registration

* The brain metastases are stable on pre-registration imaging

Patients must have completed last chemotherapy \>= 3 weeks or radiotherapy \>= 2 weeks prior to receiving study drugs

Patients must have recovered from adverse events attributable to previous treatment to =\< grade 1, except for alopecia and sensory neuropathy =\< grade 2

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

What this study is about