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