DS-1205c With Gefitinib for Metastatic or Unresectable Epidermal Growth Factor Receptor (EGFR)-Mutant Non-Small Cell Lung Cancer

Inclusion Criteria: 1. Has histologically or cytologically documented adenocarcinoma NSCLC 2. Has locally advanced or metastatic NSCLC, not amenable to curative surgery or radiation 3. Has acquired resistance to EGFR tyrosine kinase inhibitor (TKI) according to the Jackman criteria (PMID: 19949011): 1. Historical confirmation that the tumor harbors an EGFR mutation known to be associated with EGFR TKI sensitivity (including G719X, exon 19 deletion, L858R, L861Q) OR 2. Has experienced clinical benefit from an EGFR TKI, followed by systemic progression \[Response Evaluation Criteria in Solid Tumors (RECIST version 1.1) or World Health Organization (WHO)\] while on continuous treatment with an EGFR TKI 4. Is currently receiving and able to interrupt gefitinib or discontinue erlotinib, afatinib, or osimertinib 5. Has been receiving gefitinib, erlotinib, afatinib, or osimertinib for at least 6 weeks with well-controlled related toxicities less than Grade 3 in severity at the time of screening period; participants who have been receiving gefitinib must be taking gefitinib at a dose of 250 mg/day 6. Has radiological documentation of disease progression while receiving continuous treatment with gefitinib, erlotinib, afatinib, or osimertinib 7. Has at least one measurable lesion per RECIST version 1.1 8. Is willing to provide archival tumor tissue from a biopsy performed after progression during treatment with gefitinib, erlotinib, afatinib, or osimertinib OR has at least one lesion, not previously irradiated, amenable to core biopsy and is willing to undergo screening tumor biopsy 9. Demonstrates absence of EGFR T790M mutation in tumor tissue since progression during gefitinib, erlotinib, afatinib, or osimertinib treatment 10. Has Eastern Cooperative Oncology Group (ECOG) performance status (PS) of 0 or 1, with no deterioration over the previous 2 weeks Exclusion Criteria: 1. Has any evidence of small cell histology, or combined small cell and non-small cell histology, in original tumor biopsy or in screening biopsy performed since progression 2. Has previously documented evidence of anaplastic lymphoma kinase (ALK) fusion, ROS proto-oncogene 1 (ROS1) fusion, BRAF V600E mutation, rearranged during transfection (RET) rearrangement, human epidermal growth factor receptor 2 (HER2) mutation, or MET exon 14 skipping mutation - no new testing for these genomic alterations is required for Screening 3. Has received treatment with any of the following: 1. Any cytotoxic chemotherapy, immune checkpoint inhibitor therapy, investigational agent or other anticancer drug(s) from a previous cancer treatment regimen or clinical study (other than EGFR TKI), within 14 days of the first dose of study treatment 2. Immune checkpoint inhibitor therapy within 30 days of first dose of study treatment 3. Major surgery (excluding placement of vascular access) within 4 weeks of the first dose of study treatment 4. Radiotherapy treatment to more than 30% of the bone marrow or with a wide field of radiation within 4 weeks, or palliative radiation therapy within 2 weeks of the first dose of study drug treatment 4. Has history of other active malignancy within 3 years prior to enrollment, except: 1. Adequately treated non-melanoma skin cancer OR 2. Superficial bladder tumors (Tumor stage "a" \[Ta\], Tumor stage "is" \[Tis\], Tumor stage "1" \[T1\]) OR 3. Curatively treated in situ disease OR 4. Low-risk non-metastatic prostate cancer (with Gleason score \< 7 on antiandrogen therapy) 5. Has spinal cord compression or clinically active brain metastases, defined as untreated and symptomatic, or requiring therapy with corticosteroids or anticonvulsants to control associated symptoms - Subjects with clinically inactive brain metastases may be included in the study. Subjects with treated brain metastases that are no longer symptomatic and who require no treatment with corticosteroids or anticonvulsants may be included in the study if they have recovered from the acute toxic effect of radiotherapy. A minimum of 2 weeks must have elapsed between the end of whole brain radiotherapy and study enrollment (1 week for stereotactic radiotherapy). 6. Has retinal disease in the eye that is not due to neovascular age-related macular degeneration (nAMD; eg, significant diabetic retinopathy, glaucomatous retinal atrophy, retinal detachment) 7. Has history of myocardial infarction within the past 6 months 8. Has symptomatic congestive heart failure \[New York Heart Association (NYHA) Classes II-IV\], unstable angina, or cardiac arrhythmia requiring antiarrhythmic treatment 9. Has left ventricular ejection fraction (LVEF) \< 45% by either echocardiogram (ECHO) or multigated acquisition (MUGA) scan 10. Has any clinically important abnormalities in rhythm, conduction or morphology of resting ECG, eg, complete left bundle branch block, third-degree heart block, second-degree heart block, or PR interval \> 250 milliseconds (ms) 11. Has a mean corrected QT interval using Fridericia's correction (QTcF) prolongation \>470 ms for females and \>450 ms for males in three successive Screening measurements 12. Unable or unwilling to discontinue concomitant use of drugs that are known to prolong the QT interval 13. Has any factors that increase the risk of QTc prolongation or risk of arrhythmic events, such as congenital long QT. syndrome, family history of long QT syndrome or unexplained sudden death under 40 years of age in first degree relatives 14. Has a history of (non-infectious) interstitial lung disease (ILD)/pneumonitis that required corticosteroid treatment, has current ILD/pneumonitis, or has suspected ILD/pneumonitis which cannot be ruled out by imaging at screening 15. Has history of pancreatitis within the past 6 months