Inclusion Criteria:
* Participant must have histologically or cytologically confirmed non-small cell lung cancer (NSCLC) that is metastatic or unresectable. Participants must have either progressed after prior standard of care therapy (Cohorts C and hepatocyte growth factor receptor gene \[MET\]-1: epidermal growth factor receptor \[EGFR\] tyrosine kinase inhibitor \[TKI\]; Cohort D: platinum-based chemotherapy; MET-2: per regional standard of care; Cohorts wild-type adenocarcinoma (WT-Ad) and wild-type squamous cell carcinoma (WT-Sq): platinum-containing chemotherapy and programmed death- 1/ ligand-1 (PD-1/L1) therapy, either as a combined regimen or as separate lines of therapy) for metastatic disease, or be ineligible for, or have refused all other currently available therapeutic options. In cases where participants refuse currently available therapeutic options, this must be documented in the study records. For Part 1 Chemotherapy Combination Cohort only: Participants must have histologically or cytologically confirmed NSCLC that is metastatic or unresectable and be eligible for treatment with combination carboplatin and pemetrexed, in accordance with standard of care, and be willing to receive additional investigational therapy with Amivantamab
* For Part 1 Combination Dose Escalation with lazertinib only: Participants must have been diagnosed with EGFR Exon 19del or L858R activating mutation and (a) be treatment naïve for metastatic disease, without access to third generation TKI in the front-line setting, or (b) have progressed after front-line treatment with first (erlotinib or gefitinib) or second generation (afatinib) TKI and are ineligible for Cohort MET-1, or (c) have been treated with a third generation TKI (e.g., osimertinib) in either the front line or second-line setting, and are not eligible for enrollment in either Cohort C or MET-1. For Part 1 Chemotherapy Combination Cohort: Participants may be diagnosed with EGFR mutated or EGFR wild type NSCLC. For Part 2 Cohorts C, D, MET-1, and MET-2 only: Participants must also have disease with a previously diagnosed activating epidermal growth factor receptor (EGFR) mutation (includes both inhibitor sensitive primary mutations such as Exon 19 deletion and L858R (Cohort C, E, and MET-1), as well as marketed TKI-resistant mutations such as Exon 20 insertion (Cohort C, D and MET-1) or activating cMet Exon 14 skipping mutation (Cohort MET-2). Documentation of primary activating EGFR or cMet mutation eligibility by CLIA-certified laboratory (or equivalent) testing is required. For Part 2 Cohorts WT-Ad and WT-Sq: Participants must have wild-type EGFR, anaplastic lymphoma kinase (ALK), and absence of MET Exon 14 skipping mutation as tested by the Food and Drug Administration (FDA) approved test or a CLIA-certified laboratory (or equivalent). The pathology report or equivalent must be in the medical record for verification. Where testing for EGFR and ALK are not part of standard of care for participants with squamous cell carcinoma histology, documentation of the absence of these mutations is not necessary for enrollment into the WT-Sq cohort
* For Part 1: Participant must have evaluable disease. For Part 2: Participant must have measurable disease according to Response Criteria in Solid Tumors (RECIST) v1.1
* For Part 2: Cohorts A and B: Participants EGFR mutated disease must have most recently progressed following treatment with a marketed EGFR inhibitor. Exception: In participants diagnosed with mutations associated with de novo EGFR inhibitor resistance (for example, Exon 20 insertions), only previous treatment with combination platinum-based chemotherapy is required. Cohort C: Participants with primary EGFR mutated disease, with a documented EGFR alteration (example, C797S) mediating resistance to previous treatment with a third generation EGFR TKI (for example, osimertinib), in participants with primary Exon 20ins disease, the documented EGFR alteration may arise following treatment with a TKI with known activity against Exon 20ins disease (for example, poziotinib). Cohort D: participants must have been previously diagnosed with an EGFR Exon 20 insertion and have not been previously treated with a TKI with known activity against Exon 20ins disease (example, poziotinib). Cohort MET-1: Participants with documented primary EGFR mutated disease and documented MET amplification or MET mutation after progression on any EGFR TKI. Participants with disease characterized by both MET amplification and EGFR resistance mutations to prior third generation EGFR TKI will be preferentially enrolled into Cohort C. Participants may have received or have been intolerant to prior platinum-based chemotherapy. Cohort MET-2: Participants with documented primary MET Exon 14 skipping mutation non-small cell lung cancer (NSCLC). Cohort E (combination Amivantamab and lazertinib): Participants must have been diagnosed with EGFR Exon 19del or L858R activating mutation and have progressed after first or second-line treatment with a third generation TKI (e.g., osimertinib). Cohort WT-Ad: Participant must have been diagnosed with NSCLC of adenocarcinoma histology, with positive EGFR and/or MET expression as detected on a validated immunohistochemistry (IHC) assay performed by the central laboratory and have progressed on prior platinum containing chemotherapy and PD-1/L1 therapy, either as a combined regimen or as a separate line of therapy. Eligibility may be determined through IHC analysis of either archival (pre-screening) or mandatory fresh tumor tissue collected during the Screening period. Cohort WT-Sq: Participant must have been diagnosed with NSCLC of squamous cell carcinoma histology, with positive EGFR and/or MET expression as detected on a validated IHC assay performed by the central laboratory and have progressed on prior platinum-containing chemotherapy and PD-1/L1 therapy, either as a combined regimen or as a separate line of therapy. Eligibility may be determined through IHC analysis of either archival (pre-screening) or mandatory fresh tumor tissue collected during the Screening
* Participant must have Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1
Exclusion Criteria:
* Participant has uncontrolled inter-current illness, including but not limited to poorly controlled hypertension, or diabetes, ongoing or active infection, (that is, has discontinued all antibiotics for at least one week prior to first dose of study drug), or psychiatric illness/social situation that would limit compliance with study requirements. Participants with medical conditions requiring chronic continuous oxygen therapy are excluded. For Part 1 Chemotherapy Combination Cohort only: additionally, participants with active bleeding diathesis
* Participant has had prior chemotherapy, targeted cancer therapy, immunotherapy, or treatment with an investigational anticancer agent within 2 weeks or 4 half-lives whichever is longer, before the first administration of study drug. For agents with long half-lives, the maximum required time since last dose is 4 weeks. Toxicities from previous anti-cancer therapies should have resolved to baseline levels or to Grade 1 or less, (except for alopecia \[any grade\], Grade less than or equal to \[\<=\] 2 peripheral neuropathy, and Grade less than \[\<\] 2 hypothyroidism stable on hormone replacement). For Part 1 Combination Dose Escalation: Any previous treatment with systemic anti-cancer immunotherapy, including but not limited to anti-PD-1, anti-PD-L1, and anti-CTLA-4 agents. For Part 1 Chemotherapy Combination Cohort only: Any previous treatment with systemic anti-cancer immunotherapy in the past 3 months or localized radiotherapy to lung within the past 6 months. For Part 2 only: Cohorts A and B: Prior treatment with chemotherapy for metastatic disease is not allowed unless the tumor mutation carries de-novo resistance to EGFR TKI (example, Exon 20 insertions). Cohort C and MET-1: Prior treatment with more than 2 lines of cytotoxic chemotherapy for metastatic disease (maintenance therapy is not included). Cohort D: Previous treatment with an EGFR TKI with activity against EGFR Exon 20 insertions (such as poziotinib). Cohort E (combination Amivantamab and lazertinib): Any previous treatment in the metastatic setting with other than a first, second, or third generation EGFR TKI. Cohorts WT-Ad and WT-Sq: more than three lines of prior systemic therapy in the metastatic setting
* Participants with untreated brain metastases. Participants with definitively, locally-treated metastases that are clinically stable and asymptomatic for at least 2 weeks and who are off or receiving low-dose corticosteroid treatment (\<=10 mg prednisone or equivalent) for at least 2 weeks prior to study treatment are eligible. Exception: participants with asymptomatic, untreated brain metastases, each less than 1 cm in diameter, may be eligible for Amivantamab and lazertinib combination therapy in the Part 1 Combination Dose Escalation or Part 2 Combination Expansion Cohort E
* Participant has a history of malignancy other than the disease under study within 3 years before Screening (exceptions are squamous and basal cell carcinomas of the skin and carcinoma in situ of the cervix, or malignancy that in the opinion of the investigator, with concurrence with the sponsor's medical monitor, is considered cured with or minimal risk of recurrence within a year from Screening)
* Participant has not fully recovered from major surgery or significant traumatic injury prior the first dose of study drug or expects to have major surgery during the study period or within 6 months after the last dose of study drug
* Participant has, or will have, any of the following: a. An invasive operative procedure with entry into a body cavity, within 4 weeks or without complete recovery before Cycle 1 Day 1. Thoracentesis, if needed, and percutaneous biopsy for baseline tumor tissue sample may be done less than 4 weeks prior to Cycle 1 Day 1, as long as the participant has adequately recovered from the procedure prior to the first dose of study drug in the clinical judgement of the investigator; b. Significant traumatic injury within 3 weeks before the start of Cycle 1 Day 1 (all wounds must be fully healed prior to Day 1); c. Any medical condition that requires intact wound healing capacity and is expected to endanger subject safety if wound healing capacity would be severely reduced during administration of the investigational agent; d. Expected major surgery while the investigational agent is being administered or within 6 months after the last dose of study drug
