Inclusion Criteria:  ≥18 years of age at the time of signing the informed consent. Pathologically confirmed, definitively diagnosed, metastatic NSCLC harboring an activating EGFR mutation. Previously received at least 1 prior EGFR-targeted TKI. For patients enrolled to expansion Group 2, prior treatment must include an approved EGFR-targeted TKI with activity against the T790M mutation, such as osimertinib.  EGFR mutation profile determined locally via a Sponsor-approved testing methodology, using either tumor tissue (ideally from a progressing lesion) and/or ctDNA in plasma. It is preferable that samples used for analysis be obtained during or after disease progression on the last EGFR-targeted TKI received.  Dose escalation: At each dose level, slots may be reserved for patients with the mutations of interest. Expansion Groups: Patients must have NSCLC harboring EGFR T790M and C797S mutation (Group 1); EGFR T790M but not C797S (Group 2); or EGFR C797S but not T790M (Group 3).  Pretreatment tumor sample (either an archival sample or a sample obtained by pretreatment biopsy) submitted for central analysis. It is preferable that pretreatment tumor samples be obtained from a progression lesion, during or after disease progression on the last EGFR-targeted TKI received.  Patients without archival tissue available, where biopsy is not considered safe and/or medically feasible, may be discussed with the study medical monitor and may be approved for enrollment on a case-by-case basis.  Phase 2 Expansion Groups: Patient has at least 1 measurable target lesion evaluable by RECIST 1.1 as assessed by the investigator. Eastern Cooperative Oncology Group (ECOG) performance status is 0-2. Agrees to use contraception consistent with local regulations  Exclusion Criteria:  Tumor harbors any additional known primary driver alterations including but not limited to pathologic abnormalities of EGFR exon 20, KRAS, BRAF V600E, NTRK1/2/3, HER2, ALK, ROS1, MET, or RET. NSCLC with mixed squamous cell histology as well as tumors with histologic transformation (NSCLC to SCLC and with epithelial to mesenchymal transition).  Received the following anticancer therapy:  EGFR-targeted TKI within 7 days prior to the first dose of study drug. Any immunotherapy or other antibody therapy (including EGFR-targeted antibodies or bi-specific antibodies) within 28 days prior to the first dose of study drug (immune-related toxicities must have resolved to < Grade 2 prior to starting BLU 945). 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 945 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. Participant received 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. 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 untreated CNS and leptomeningeal disease is allowed and, when measurable, should be captured as target lesions.  Any of the following abnormalities on the latest laboratory test prior to the first dose of study drug (ie, within 7 days prior to Cycle 1 Day 1 [C1D1]):  Absolute neutrophil count (ANC) <1.0×109/L. Platelet count <75×109/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) >3× 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) or measured creatinine clearance <40 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. Known intracranial hemorrhage and/or bleeding diatheses. 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. Patients with prior ILD associated with clinically resolved COVID 19 infection may be enrolled upon discussion with, and approval by, the Medical Monitor. 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 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. Mean resting QT interval corrected using Fridericia's formula (QTcF) >470 msec, a history of prolonged QT syndrome or Torsades de pointes, or a familial history of prolonged QT syndrome. 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 (eg, Type II second degree heart block or third degree heart block).  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, the following categories of patients with prior malignancy are eligible to participate:  Patients with a previous malignancy that completed all anticancer treatment at least 2 years before and with no evidence of residual disease from the prior malignancy at registration Patients who have another concurrent malignancy (not lung cancer) that is clinically stable and does not require tumor-directed treatment. (Examples include, but are not limited to, completely resected basal cell carcinoma and squamous cell carcinoma of skin, curatively treated prostate cancer, and early gastric cancer cured by endoscopic mucosal resection or endoscopic submucosal dissection.) Active, uncontrolled infection (viral, bacterial, or fungal) or active tuberculosis, hepatitis B, hepatitis C, AIDS-related illness, or known COVID 19 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 may be eligible if benefit/risk is justified and permission is granted from the Sponsor. Received neutrophil or platelet growth factor support within 14 days of the first dose of study drug. Requires treatment with a prohibited medication or herbal remedy (as specified in Appendix 2) that cannot be discontinued at least 2 weeks before the start of study drug administration. BLU 945 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. 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).