Afatinib and Necitumumab in Patients With EGFR Mutation Positive Advanced or Metastatic Non-small Cell Lung Cancer

Inclusion Criteria: * Signed and dated written informed consent * Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1 or 2 * Histologically or cytologically-confirmed advanced or metastatic non-small cell lung cancer (NSCLC) that is EGFR mutation positive; rare sensitizing mutations allowed * Progression on a first generation EGFR TKI (T790M negative), or progression on a third generation TKI (if T790M positive at time of progression on a first or second generation TKI) * At least one measurable lesion as defined by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 that can be followed by computed tomography (CT) or magnetic resonance imaging (MRI) * Patient consents to undergo a medically safe tumor biopsy at time of disease progression for mutation analysis * Leukocytes \>= 3,000/uL * Absolute neutrophil count (ANC) \>= 1,500/uL * Platelets \>= 100,000/uL * Hemoglobin \>= 9 g/dL * Serum albumin \>= 2.5 g/dL * Calculated creatinine clearance \> 50 mL/min (per the Cockcroft-Gault formula) * Total bilirubin =\< 1.5 times upper limit of normal (ULN) * Alkaline phosphatase (ALP) =\< 3.0 x ULN * Alanine aminotransferase (ALT) and aspartate transaminase (AST) =\< 3.0 x ULN; for patients with hepatic metastases, ALT and AST =\< 5.0 x ULN are acceptable \* Note: if a patient experiences elevated ALT \> 5 x ULN and elevated total bilirubin \> 2 x ULN, clinical and laboratory monitoring should be initiated by the investigator; for patients entering the study with ALT \> 3 x ULN, monitoring should be triggered at ALT \> 2 x baseline * Women of childbearing potential (WOCBP) must have a negative serum pregnancy test within 14 days prior to receiving first dose of study medication; and additionally agree to use at least two methods of birth control or abstain from heterosexual intercourse from the time of signing consent, and until 6 months after patient's last dose of study drug \* WOCBP of childbearing potential are defined as those not surgically sterile or not post-menopausal (i.e. if a female patient has not had a bilateral tubal ligation, a bilateral oophorectomy, or a complete hysterectomy; or has not been amenorrheic for 24 months in the absence of an alternative medical cause, then patient will be considered a female of childbearing potential); postmenopausal status in females under 55 years of age should be confirmed with a serum follicle-stimulating hormone (FSH) level within laboratory reference range for postmenopausal women * WOCBP must agree to follow instructions for method(s) of contraception from the time of signing consent and until 6 months after last dose of study therapy * Men able to father children who are sexually active with WOCBP must agree to follow instructions for method(s) of contraception from the time of signing consent and until 6 months after last dose of study therapy; men able to father children are defined as those who are not surgically sterile (i.e. patient has not had a vasectomy) Exclusion Criteria: * Prior treatment against NSCLC with an EGFR monoclonal antibody * Prior afatinib therapy, unless patient received an intervening third generation EGFR TKI after concluding prior afatinib and before enrollment on this clinical study * Less than 3 days from prior treatment with EGFR TKI; patients with adverse events related to prior EGFR TKI must recover to Common Terminology Criteria for Adverse Events (CTCAE) =\< grade 1 to be eligible * History of arterial or venous thromboembolism within 3 months prior to study enrollment; patients with a history of venous thromboembolism beyond 3 months prior to study enrollment can be enrolled if they are appropriately treated with low molecular weight heparin * Subjects with a history of interstitial lung disease (e.g., sarcoidosis) that is symptomatic or may interfere with the detection or management of suspected drug-related pulmonary toxicity; subjects with chronic obstructive pulmonary disease (COPD) whose disease is controlled at study entry are allowed * Symptomatic brain metastases; stable and treated central nervous system (CNS) disease allowed; patients with treated, asymptomatic brain metastases are eligible if there has been no change in brain disease status for at least two (2) weeks prior to initiating study treatment; anticonvulsant therapy will be allowed if patient is on a stable or decreasing dose of anticonvulsant treatment for at least two (2) weeks prior to initiating study treatment * Subjects with carcinomatous meningitis * Prior radiotherapy or radiosurgery \< 2 weeks prior to starting study treatment * Current symptomatic congestive heart failure (New York Heart Association classification \>= grade III), unstable cardiac arrhythmia requiring therapy (e.g. medication or pacemaker), unstable angina (e.g. new, worsening or persistent chest discomfort), or uncontrolled hypertension (systolic \> 160 mmHg or diastolic \> 100 mmHg); or any of the following occurring within 6 months (180 days) prior to first dose of study treatment: myocardial infarction, coronary/peripheral artery bypass graft, cerebrovascular accident or transient ischemic attack; use of antihypertensive medication to control blood pressure is allowed * Patient is pregnant or breastfeeding, or plans to become pregnant or father children from time of signing consent and lasting until 6 months after the last dose of trial treatment * Previous or concomitant malignancies at other sites, except effectively treated non-melanoma skin cancers, carcinoma in situ of the cervix, ductal carcinoma in situ or effectively treated malignancy that has been in remission for more than 3 years and is considered to be cured AND no additional therapy is ongoing and required during the study period with the exception of bisphosphonates and anti-androgens and/or gonadorelin analogues for the treatment of prostate cancer are permitted; subjects with other active malignancy requiring concurrent intervention are excluded * Requiring treatment with any of the prohibited concomitant medications listed that cannot be stopped for the duration of trial participation * Any history or presence of poorly controlled gastrointestinal disorders that could affect the absorption of the study drug (e.g. Crohn's disease, ulcerative colitis, chronic diarrhea, malabsorption) * Recent (within 30 days before enrollment) or concurrent yellow fever vaccination * All toxicities attributed to prior anti-cancer therapy other than alopecia, fatigue, or peripheral neuropathy must have resolved to grade 1 (National Cancer Institute \[NCI\] CTCAE version 4) or baseline before administration of study drug * The patient has any ongoing or active infection, including active tuberculosis; Note: a urinary tract infection controlled with oral antibiotics initiated at least 7 days prior to study entry is acceptable * Known positive test for hepatitis B, hepatitis C, human immunodeficiency virus (HIV), or acquired immunodeficiency syndrome (AIDS) * The patient has a known allergy/history of hypersensitivity reaction to any of the treatment components, including any ingredient used in the formulation of necitumumab, or any other contraindication to one of the administered treatments * Known hypersensitivity to afatinib or the excipients of any of the trial drugs * History of severe hypersensitivity reactions to other monoclonal antibodies * Subjects who are compulsorily detained for treatment of either a psychiatric or physical (e.g. infectious disease) illness * Any other serious or uncontrolled medical disorder, active infection, physical exam finding, laboratory finding, altered mental status, or psychiatric condition that, in the opinion of the investigator, would limit a subject's ability to comply with the study requirements, substantially increase risk to the subject, or impact the interpretability of study results