Inclusion Criteria:  ≥18 years of age at the time of signing the informed consent. Pathologically confirmed metastatic NSCLC.  The following EGFR mutation profile determined locally via a Sponsor-approved testing methodology, using either tumor tissue (preferably from a progressing lesion) and/or ctDNA in plasma, preferably obtained during or after disease progression on the last EGFR-targeted TKI received:  All Parts: activating EGFR mutation (Ex19Del or L858R) Part 2A: Tumor must additionally harbor an EGFR C797X resistance mutation.  Previously received:  Part 1A and 2A: At least 1 prior third-generation EGFR-targeted TKI, such as osimertinib  Part 1B: Patients must have experienced progressive disease while on osimertinib, were able to tolerate prior osimertinib 80 mg QD dose, and continuing on osimertinib is deemed to be in the patient's best interests in the opinion of the Investigator.  Patients who have discontinued osimertinib may be eligible, if no more than 6 weeks elapse between the discontinuation of prior osimertinib and resumption of osimertinib on study.  Part 1C: At least 1 prior EGFR-targeted TKI  Willing to provide pretreatment tumor sample (either an archival sample or a sample obtained by pretreatment biopsy [preferably from a progressing lesion and preferably obtained during or after disease progression on the last EGFR-targeted TKI received]).  Patients without available archival tissue and/or where biopsy is not considered safe and/or medically feasible, may be discussed with the study medical monitor and approved for enrollment on a case-by-case basis.  Part 2A: at least 1 measurable target lesion per RECIST 1.1 as assessed by the Investigator Eastern Cooperative Oncology Group (ECOG) performance status 0-1. Agrees to use contraception consistent with local regulations  Exclusion Criteria:  Have disease that is suitable for local therapy administered with curative intent. Have tumor that harbors EGFR T790M mutation or any additional known driver alterations (including but not limited to, EGFR exon 20 insertions, or pathologic abnormalities of KRAS, BRAF V600E, NTRK1/2/3, HER2, ALK, ROS1, MET, or RET). Have NSCLC with mixed cell histology or a tumor with known histologic transformation (NSCLC to SCLC, SCLC to NSCLC, or epithelial to mesenchymal transition).  Have received the following anticancer therapy:  Any third-generation EGFR TKI (such as osimertinib) within 7 days prior to the planned first dose of study drug. Note: patients in Part 1B do not require a wash-out period for osimertinib. Part 2A: Previous therapy with first- or second-generation EGFR TKI, such as erlotinib, gefitinib, afatinib or dacomitinib. Part 1C: Prior platinum-based chemotherapy for advanced or metastatic disease. Any immunotherapy or other antibody therapy (including EGFR-targeted antibodies or bi-specific antibodies) within 21 days prior to the first dose of study drug. Any other systemic anticancer therapy within 14 days or 5 half-lives prior to the first dose of study drug, whichever is the shortest, but with a minimum of 7 days in all circumstances. BLU-701 may be started within these washout periods if considered by the Investigator to be safe and within the best interest of the patient, with prior Sponsor approval. Radiotherapy to a large field or including a vital organ (including whole brain radiotherapy or stereotactic radiosurgery to brain) within 14 days before the first dose of study drug. Radiotherapy to a focal site of disease that did not include a vital organ (such as a limb) within 7 days before the first dose of study drug. Have CNS metastases or spinal cord compression that is associated with progressive neurological symptoms or requires increasing doses of corticosteroids to control the CNS disease. If a patient requires corticosteroids for management of CNS disease, the dose must have been stable for the 2 weeks preceding treatment. Asymptomatic CNS and leptomeningeal disease is allowed and, when measurable, should be captured as target lesions.  Have any of the following laboratory abnormalities on last laboratory assessment prior to initiation of study drug (i.e., C1D1 or Screening):  Absolute neutrophil count (ANC) <1.0×109/L (for patients in Part 1C: <1.5×109/L) Platelet count <75×109/L (for patients in Part 1C: <100×109/L) Hemoglobin ≤8.0 g/dL (red blood cell transfusion and erythropoietin may be used to reach at least 8.0 g/dL but must have been administered at least 2 weeks prior to the first dose of study drug). Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) >2.5× the upper limit of normal (ULN) if no hepatic metastases are present; >5× ULN if hepatic metastases are present. Total bilirubin >1.5× ULN; >3× ULN in presence of Gilbert's disease. Estimated (Cockroft-Gault formula, Appendix 1) or measured creatinine clearance <60 mL/min. International normalized ratio (INR) >2.3 or prothrombin time (PT) >6 seconds above control or a patient-specific INR or PT abnormality that the treating investigator considers clinically relevant and/or increases the risk for hemorrhage in that individual patient. Have known intracranial hemorrhage and/or bleeding diatheses. Have clinically active ongoing interstitial lung disease (ILD) of any etiology, including drug-induced ILD, and radiation pneumonitis within 28 days prior to initiation of study treatment. Grade 1 asymptomatic ILD is not exclusionary. Have any unresolved toxicities from prior therapy greater than Common Terminology Criteria for Adverse Events (CTCAE) Grade 1 or that have not resolved to baseline at the time of starting the study. Exceptions include alopecia and fatigue, and, upon discussion with and approval by the Medical Monitor, other toxicities that are not thought to present a risk to patient safety. Have mean resting QT interval corrected using Fridericia's formula (QTcF) >450 msec, a history of prolonged QT syndrome or Torsades de pointes, or a familial history of prolonged QT syndrome. Have clinically significant, uncontrolled, cardiovascular disease including congestive heart failure Grade III or IV according to the New York Heart Association classification; myocardial infarction or unstable angina within the previous 6 months, uncontrolled hypertension, or clinically significant, uncontrolled arrhythmias, including bradyarrhythmia that may cause QT prolongation (e.g., Type II second degree heart block or third degree heart block). Have history of another primary malignancy (other than completely resected carcinomas in situ) that has been diagnosed or required therapy within 2 years prior to initiation of study treatment. However, upon discussion with the Sponsor, patients who have another concurrent malignancy (not lung cancer) that is clinically stable and does not require tumor-directed treatment may be eligible to participate. Examples include, but are not limited to, completely resected basal cell carcinoma and squamous cell carcinoma of skin; curatively treated prostate cancer, breast cancer; and early gastric cancer cured by endoscopic mucosal resection or endoscopic submucosal dissection. Have active, uncontrolled infection (viral, bacterial, or fungal), including tuberculosis, hepatitis B, hepatitis C, AIDS-related illness, or COVID19 infection. Controlled infections, including HIV and "cured" hepatitis C (no active fever, no evidence of systemic inflammatory response syndrome) that are stable on antiviral treatment are not exclusionary. For Parts 1A, 1B, and 1C: have received neutrophil or platelet growth factor support within 14 days of the first dose of study drug. Require treatment with a prohibited medication or herbal remedy that cannot be discontinued at least 2 weeks before the start of study drug administration. BLU-701 may be started within 14 days or 5 half-lives of these therapies if considered by the Investigator to be safe and within the best interest of the patient, with prior Sponsor approval. Have major surgical procedure within 14 days of the first dose of study drug (procedures such as central venous catheter placement, tumor needle biopsy, and feeding tube placement are not considered major surgical procedures).