HER3-DXd (Patritumab Deruxtecan; U3-1402) in Combination With Osimertinib in Subjects With Locally Advanced or Metastatic EGFR-mutated Non-Small Cell Lung Cancer

Inclusion Criteria: Inclusion Criteria Specific to Dose Escalation and Second-line Dose Expansion: * Documentation of EGFR exon 19 deletion or L858R mutation detected from tumor tissue * Must have received osimertinib for locally advanced or metastatic disease at a dose of 80 mg once daily (QD) for at least 6 weeks and must not miss more than two doses during the 2 weeks prior to the first day of study treatment (Cycle 1, Day 1) * Must not have received any other prior systemic cancer therapies in the locally advanced/metastatic setting * Has documentation of radiological disease progression following first-line treatment with osimertinib in the locally advanced or metastatic setting Inclusion Criteria Specific to First-line Dose Expansion: * The tumor tissue harbors one of the 2 common EGFR mutations occurring in NSCLC known to be associated with EGFR-TKI sensitivity (exon 19 deletion or L858R) as assessed by Clinical Laboratory Improvement Amendments (CLIA)-certified (United States \[US\] sites), accredited (outside of the US), local laboratory or central laboratory. Only tissue-based testing will be accepted. * Participants must have previously untreated locally advanced or metastatic NSCLC and must be eligible to receive first-line treatment with osimertinib, according to the judgment of the investigator. Prior adjuvant or neo-adjuvant therapy (chemotherapy, radiotherapy, investigational agents; except with osimertinib) is permitted. All Participants: Participants must meet all criteria to be eligible for inclusion in this study: * Histologically or cytologically documented locally advanced or metastatic NSCLC not amenable to curative surgery or radiation. * At least 1 measurable lesion as assessed by Investigator as per Response Evaluation Criteria in Solid Tumors (RECIST v1.1) * Tissue requirements * For Dose Escalation (all cohorts): provide an optional pre-treatment tumor tissue of sufficient quantity, as defined in the laboratory manual. The optional pre-treatment tumor tissue can be provided as either: * Pre-treatment tumor biopsy from at least 1 lesion not previously irradiated and amenable to core biopsy OR * Archival tissue collected from a biopsy performed prior to signing of the tissue consent, and since progression while on treatment with the most recent cancer therapy * For First-line Dose Expansion (Cohorts 3, 4a, and 4b): provide an optional pre-treatment and optional on-treatment tumor tissues of sufficient quantity, as defined in the laboratory manual. The optional pre-treatment tumor tissue can be provided as either: * Pre-treatment tumor biopsy from at least 1 lesion not previously irradiated and amenable to core biopsy OR * Archival tissue collected from a biopsy performed at the time of initial diagnosis or later * For Second-line Dose Expansion (Arm 1, Arm 2, and Arm 1b): provide a required pre-treatment and required on-treatment tumor tissues of sufficient quantity, as defined in the laboratory manual. The required pre-treatment tumor tissue can be provided as either: * Pre-treatment tumor biopsy from at least 1 lesion not previously irradiated and amenable to core biopsy OR * Archival tissue collected from a biopsy performed prior to signing of the tissue consent, and since progression while on treatment with the most recent cancer therapy regimen * Note: For all participants who consent to a pre-treatment biopsy, in order to ensure an adequate amount of tissue is available, a core needle biopsy is required. * Has adequate bone marrow reserve and organ function based on local laboratory data within 14 days prior to Cycle 1, Day 1 (Dose Escalation and First-line Dose Expansion) or within 14 days prior to randomization (Second-line Dose Expansion): * Platelet count: ≥100 000/mm\^3 or ≥100 × 10\^9/L (platelet transfusions are not allowed within 14 days prior to the assessment of platelets during the screening period in order to meet the study inclusion criterion) * Hemoglobin: ≥9.0 g/dL (transfusion of red blood cells and/or growth factor support is not allowed within 14 days prior to the assessment of hemoglobin during the screening period in order to meet the study inclusion criterion) * Absolute neutrophil count (ANC): 1500/mm\^3 or ≥1.5 × 10\^9/L (granulocyte colony stimulating factor support is not allowed within 14 days prior to the assessment of ANC during the screening period in order to meet the study inclusion criterion) * Creatinine clearance (CrCl): CrCl ≥30 mL/min as calculated using the Cockcroft-Gault equation or measured CrCl * Aspartate aminotransferase/ alanine aminotransferase: ≤3 × ULN (if liver metastases are present, ≤5 × ULN) * Total bilirubin: ≤1.5 × ULN if no liver metastases (\<3 × ULN in the presence of documented Gilbert's syndrome \[unconjugated hyperbilirubinemia\] or liver metastases) * Serum albumin: ≥2.5 g/dL * Alkaline phosphatase (ALP) and Gamma-glutamyl transferase (GGT): ≤2.5 × ULN of both ALP and GGT * Prothrombin time (PT) or PT-international normalized ratio (INR) and Activated partial thromboplastin time (aPTT) / Partial thromboplastin time (PTT): ≤1.5 × ULN, except for subjects on coumarin-derivative anticoagulants or other similar anticoagulant therapy, who must have PT-INR within therapeutic range as deemed appropriate by the Investigator. Exclusion Criteria: * Any previously documented histologic or cytologic evidence of small cell OR combined small cell/non-small cell disease * Has a history of (non-infectious) interstitial lung disease (ILD)/pneumonitis that required corticosteroid therapy, has current ILD, or is suspected to have such disease by imaging during screening. * Clinically severe pulmonary compromise (based on Investigator's assessment) resulting from intercurrent pulmonary illnesses including, but not limited to: * Any underlying pulmonary disorder (eg, pulmonary emboli within three months of the study enrollment or randomization, severe asthma, severe chronic obstructive pulmonary disease, restrictive lung disease, pleural effusion); * Any autoimmune, connective tissue or inflammatory disorders with pulmonary involvement (eg, rheumatoid arthritis, Sjogren's syndrome, sarcoidosis); OR prior complete pneumonectomy. * Is receiving chronic systemic corticosteroids dosed at \>10 mg prednisone or equivalent anti-inflammatory activity or any form of immunosuppressive therapy prior to Cycle 1, Day 1. Participants who require use of bronchodilators, inhaled or topical steroids, or local steroid injections may be included in the study. * Evidence of any leptomeningeal disease. * Has spinal cord compression or clinically active central nervous system metastases, defined as symptomatic, or requiring therapy with corticosteroids or anticonvulsants to control associated symptoms. Participants with clinically inactive brain metastases may be included in the study. Participants with treated brain metastases who are no longer symptomatic and who require no treatment with corticosteroids or anticonvulsants may be included in the study, but must have a stable neurologic status for at least 4 weeks prior to Cycle 1, Day 1. Participants with asymptomatic brain metastases and treated with anticonvulsants as prophylaxis are able to enroll following a 14-day washout period. Note: A CT or MRI scan of the brain at baseline is required for all participants. * Inadequate washout period prior to Cycle 1, Day 1 defined as: * Whole brain radiation therapy \<28 days or stereotactic brain radiation therapy \<7 days; * Any systemic anticancer therapy (excluding osimertinib in all Dose Escalation Cohorts and in Second-line Dose Expansion \[Arm 1, Arm 2, and Arm 1b\]), including investigational agents, \<14 days or 5 half-lives, whichever is longer * Immune checkpoint inhibitor therapy ≤21 days * Major surgery (excluding placement of vascular access) \<4 weeks * Radiotherapy treatment to more than 30% of the bone marrow or with a wide field of radiation \< 28 days or palliative radiation therapy \<7 days * Chloroquine or hydroxychloroquine ≤14 days * Medications or herbal supplemented known to be strong inducers of cytochrome P450 (CYP) 3A4 \<21 days. * Has unresolved toxicities from previous anticancer therapy, defined as toxicities (other than alopecia) not yet resolved to National Cancer Institute Common Terminology Criteria for Adverse Events (NCI-CTCAE) version 5.0, Grade ≤1 or baseline. Subjects with chronic Grade 2 toxicities may be eligible per the discretion of the Investigator after consultation with the Sponsor Medical Monitor or designee. * Refractory nausea and vomiting, chronic gastrointestinal diseases, inability to swallow osimertinib, or previous significant bowel resection that would preclude adequate absorption of osimertinib. * Has any primary malignancy other than locally advanced or metastatic NSCLC within 3 years prior to Cycle 1, Day 1 (Dose Escalation and First-line Dose Expansion) or within 3 years prior to randomization (Second-Line Dose Expansion), except adequately resected non-melanoma skin cancer, curatively treated in situ disease, or other solid tumors curatively treated. * Uncontrolled or significant cardiovascular disease prior to Cycle 1, Day 1 including: * Mean corrected QT interval using Fridericia's formula (QTcF) interval of \>450 ms in 3 successive central screening measurements * Left ventricular ejection fraction (LVEF) ≤50% by either echocardiogram (ECHO) or multigated acquisition (MUGA) scan * Resting systolic blood pressure \>180 mmHg or diastolic blood pressure \>110 mmHg * Myocardial infarction within 6 months * New York Heart Association (NYHA) Classes 2 to 4 congestive heart failure within 28 days * Uncontrolled angina pectoris within 6 months * Has cardiac arrhythmia requiring antiarrhythmic treatment * Complete left or right bundle branch block within 6 months * History of second- or third-degree heart block or PR interval \>250 ms within 6 months * History of clinically relevant ventricular arrhythmias, such as ventricular tachycardia, ventricular fibrillation, or Torsade de Pointes * Has any factors that increase the risk of corrected QT (QTc) prolongation or risk of arrhythmic events, such as heart failure, hypokalemia, congenital long QT syndrome, family history of long QT syndrome, or unexplained sudden death under 40 years of age in first-degree relatives, or any concomitant medication known to prolong the QT interval * Has clinically significant corneal disease * Any evidence of severe or uncontrolled diseases including active bleeding diatheses, active infection, psychiatric illness/social situations, geographical factors, substance abuse, or other factors which in the Investigator's opinion makes it undesirable for the subject to participate in the study or which would jeopardize compliance with the protocol. Screening for chronic conditions is not required. * Has a known human immunodeficiency virus (HIV) infection that is not well controlled.