A Study of Amivantamab and Lazertinib in People With Non-Small Cell Lung Cancer (NSCLC)

Inclusion Criteria: * Age ≥18 years * Written informed consent * Advanced biopsy-proven metastatic or recurrent non-small cell lung cancer * Somatic activating mutation in EGFR in a prior tumor biopsy or cfDNA sample * Patients will have progressed on standard of care therapies * Patients with EGFR exon 20 insertions will have progressed on platinum-based chemotherapy * Patients with EGFR alterations sensitizing to tyrosine kinase inhibitors (TKIs) will have progressed on osimertinib * Patients will be allowed to have received other systemic therapies since progression on the above, including investigational agents at least 28 days or 5 half lives prior to the first dose of study drug, whichever is shorter * Subjects must have at least one measurable (at least 5 mm) intracranial metastasis lesion. For lesions ≥5 mm and \<10 mm RANO-BM will be used. For Lesions \> 10 mm (1cm) RECIST 1.1 criteria will be used. * For Cohort A, subjects must have new or progressing CNS metastases. Extracranial measurable disease is not required. * For Cohort B, subjects must have evidence of LM involvement by positive CSF cytology or presence of CTCs in CSF. Extracranial measurable disease is not required. * Recent extracranial tissue biopsy within 8 weeks of C1D1 or willingness to undergo a repeat tumor biopsy. If subjects do not have an extracranial lesion amenable to biopsy, this requirement may be waived. * Karnofsky performance status (KPS) ≥60% * Ability to swallow oral medications * Adequate organ function * Hemoglobin ≥ 9 g/dL * Platelets ≥ 75 x 10\^9/L * Absolute neutrophil count (ANC) \>1.5 x 10\^9/L * AST, ALT ≤ 3 x ULN (if liver metastases are present, ≤5 × ULN) * Total bilirubin ≤1.5 x ULN if no liver metastases or \<3 × ULN in the presence of documented Gilbert's Syndrome (unconjugated hyperbilirubinemia) or liver metastases; subjects with Gilbert's syndrome can enroll if conjugated bilirubin is within normal limits * Serum creatinine \<1.5 x ULN or if available, measure creatine clearance \>50mL/min/1.73 m\^2 using the Cockcroft-Gault equation * Before enrollment, a women must be either: * Not of childbearing potential: premenarchal; postmenopausal (\>45 years of age with amenorrhea for at least 12 months); permanently sterilized (e.g., bilateral tubal occlusion \[which includes tubal ligation procedures as consistent with local regulations\], hysterectomy, bilateral salpingectomy, bilateral oophorectomy); or otherwise be incapable of pregnancy * Of childbearing potential and practicing effective method(s) of birth control consistent with local regulations regarding the use of birth control methods for subjects participating in clinical studies, as described below: * Practicing true abstinence (when this is in line with the preferred and usual lifestyle of the subject), which is defined as refraining from heterosexual intercourse during the entire period of the study, including up to 6 months after the last dose of study drug is given. Periodic * abstinence (calendar, symptothermal, post-ovulation methods) is not consider an acceptable contraceptive method * Have a sole partner who is vasectomized * Practicing 2 methods of contraception, including one highly effective method (i.e., established use of oral, injected or implanted hormonal methods of contraception; placement of intrauterine device \[IUD\] or intrauterine system \[IUS\], AND, a second method (e.g., condom with spermicidal foam/gel/film/cream/suppository or collusive cap \[diaphragm or cervical/vault caps\] with spermicidal foam/gel/film/ cream/suppository) * Subjects must agree to continue contraception throughout the study and continuing through 6 months after the last dose of study drug * NOTE: If the childbearing potential changes after start of the study (e.g., woman who is not heterosexually active becomes active, premenarchal woman experiences menarche) the woman must begin a highly effective method of birth control, as described above. * A woman of childbearing potential must have a negative serum (b-human chorionic gonadotropin \[b-hCG\]) at Screening * A woman must agree not to donate eggs (ova, oocytes) for the purposes of assisted reproduction during the study and for 6 months after receiving the last dose of study drug * A man who is sexually active with a woman of childbearing potential must agree to use a condom with spermicidal foam/gel/film/cream/suppository and his partner must also be practicing a highly effective method of contraception (i.e., established use of oral, injected or implanted hormonal methods of contraception; placement of an intrauterine device \[IUD\] or intrauterine system \[IUS\]). If the subject is vasectomized, he must still use a condom (with or without spermicide), but his female partner is not required to use contraception. The subject must also not donate sperm during the study and for 6 months after receiving the last dose of study drug Exclusion Criteria: * Pregnant or lactating women * Any radiotherapy within 1 week of starting treatment on protocol * Any major surgery within 1 week of starting treatment on protocol * Clinically significant toxicities from previous treatment * Previous systemic chemotherapy within 2 weeks of starting treatment on protocol * EGFR TKI or other oral treatment within 3 days of starting treatment on protocol * Interstitial lung disease (ILD), including drug-induced ILD or radiation pneumonitis requiring prolonged steroids or other immune suppressive agents that is unresolved or resolved within the last 3 months * Progressive neurological symptoms requiring escalating doses of steroids or not controlled with steroids * Positive hepatitis B (hepatitis B virus \[HBV\]) surface antigen (HBsAg) * NOTE: Subjects with a prior history of HBV demonstrated by positive hepatitis B core antibody are eligible if they have at Screening 1) a negative HBsAg and 2) a HBV DNA (viral load) below the lower limit of quantification, per local testing. Patients who fit these criteria must use Hep B prophylaxis during treatment. Subjects with a positive HBsAg due to recent vaccination are eligible if HBV DNA (viral load) is below the lower limit of quantification, per local testing * Positive hepatitis C antibody (anti-HCV) * NOTE: Subjects with a prior history of HCV, who have completed antiviral treatment and have subsequently documented HCV RNA below the lower limit of quantification per local testing are eligible * Other clinically active or chronic liver disease * Participant is positive for human immunodeficiency virus (HIV), with 1 or more of the following: * Receiving ART that may interfere with study treatment (consult sponsor for review of medication prior to enrollment) * CD4 count \<350 at screening * AIDS-defining opportunistic infection within 6 months of start of screening * Not agreeing to start ART and be on ART\>4 weeks plus having HIV viral load \<400 copies/mL at end of 4-week period (to ensure ART is tolerated and HIV controlled * Participant has active cardiovascular disease including, but not limited: * A medical history of deep vein thrombosis or pulmonary embolism within 1 month prior to randomization or any of the following within 6 months prior to randomization: myocardial infarction, unstable angina, stroke, transient ischemic attack, coronary/peripheral artery bypass graft, or any acute coronary syndrome. Clinically non-significant thrombosis, such as non-obstructive catheter-associated thrombus, incidental or asymptomatic pulmonary embolism, are not exclusionary. * Uncontrolled (persistent) hypertension: systolic blood pressure \>160 mm Hg; diastolic blood pressure \>100 mm Hg. * Congestive heart failure (CHF), defined as New York Heart Association (NYHA) class IIIIV or hospitalization for CHF (any NYHA class; refer to Appendix 3: New York Heart Association Criteria) within 6 months of randomization * Participant has a significant genetic predisposition to venous thromboembolic (VTE) events such as Factor V Leiden. * Participant has a prior history of VTE and is not on appropriate therapeutic anticoagulation as per NCCN or local guidelines * Participant has an uncontrolled illness, including but not limited to: * Uncontrolled diabetes * Ongoing or active infection (includes infection requiring treatment with antimicrobial therapy \[participants will be required to complete antibiotics 1 week prior to starting study treatment\] or diagnosed or suspected viral infection. * Active bleeding diathesis * Impaired oxygenation requiring continuous oxygen supplementation * Refractory nausea and vomiting, chronic gastrointestinal diseases, inability to swallow the formulated product, or previous significant bowel resection that would preclude adequate absorption of study treatment * Psychiatric illness, social situation, or any other circumstances that would limit compliance with study requirements * Any ophthalmologic condition that is clinically unstable * Pulmonary embolism (PE) and deep vein thrombosis (DVT), within 1 month of start of study drug * Myocardial infarction, unstable angina, stroke, transient ischemic attach (TIA), or coronary/peripheral artery bypass graft, or any acute coronary syndrome within 6 months of start of study drug * Congestive heart failure defined as New York Heart Association (NYHA) Class III-IV or hospitalization for congestive heart failure (any NYHA class) within 6 months of study Day 1 * Prolonged QTcF interval \>480 msec or clinically significant cardiac arrhythmia or electrophysiologic disease (e.g., placement of implantable cardioverter defibrillator or atrial fibrillation with uncontrolled rate). Note: Subjects with cardiac pacemakers who are clinically stable are eligible * Immune-mediated rash from checkpoint inhibitors that has not resolved to grade 1 prior to enrollment * Contraindication or inability to undergo serial MRIs * Recent use of amiodarone, phenobarbitone, and other prohibited medications * Participant has concurrent or prior malignancy other than the disease under study. The following exceptions require consultation with the Medical Monitor: * Non-muscle invasive bladder cancer (NMIBC) treated within the last 24 months that is considered completely cured. * Skin cancer (non-melanoma or melanoma) treated within the last 24 months that is considered completely cured. * Non-invasive cervical cancer treated within the last 24 months that is considered completely cured. * Participant had major surgery excluding placement of vascular access or tumor biopsy, or had significant traumatic injury within 4 weeks before randomization, or will not have fully recovered from surgery, or has surgery planned during the time the participant is expected to participate in the study * Participant is currently receiving medications or herbal supplements known to be potent CYP3A4/5 inducers and is unable to stop use for an appropriate washout period prior to enrollment. * Note: Participants with planned surgical procedures to be conducted under local anesthesia may participate