PSMA-High: EBRT/ PSMA617/ ADT vs. EBRT/ ADT

Inclusion Criteria: * Patient must have high-risk prostate cancer (HRPC) defined by presence of exactly one high-risk feature: cT3a OR Grade Group 4 or 5 OR PSA \> 20 ng/mL. * Histologic confirmation of adenocarcinoma of the prostate. * Patient must have localized HRPC defined by conventional imaging (no N1 disease by CT or MRI). Patients with or without intra-pelvic nodal metastases by PSMA-PET may be included as long as not enlarged \>10mm short axis by conventional CT size criteria. * Patients must have PSMA-PET (68Ga-PSMA-11 or 18F-DCFPyL) with prostate tumor SUVmax \> 10. * Patient must qualify for definitive treatment of prostate cancer including EBRT as well as ADT (up to 45 days of prior ADT is allotted). * Patient must be ≥ 18 years of age. * Patient must have a life expectancy ≥ 24 months. * Patient must have an Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2. * Adequate bone marrow reserve and organ function as demonstrated by complete blood count and chemistry panel completed within the prior 6 weeks demonstrating: 1. Platelet count of \>100 x109/L 2. White blood cell (WBC) count \> 3,000/mL 3. Neutrophil count of \> 1,500/mL 4. Hemoglobin ≥ 10 g/dL 5. Estimated glomerular filtration rate (eGFR) \> 50 mL/min based upon Chronic Kidney Disease-Epidemiology Collaboration (CKD-EPI) equation. Due to safety concerns relating to renal clearance and toxicity of 177Lu-PSMA-617, patients with estimated GFR between 50 - 60 mL/min will require a 99mTc-TPA GFR test and only patients with non-obstructive pathology will be included in the study. 6. Total bilirubin \< 3 x ULN (except if confirmed history of Gilbert's disease) 7. Serum albumin \> 30 g/L 8. Aspartate aminotransferase (AST) \< 3 times the ULN * For male patients with partners of childbearing potential, agreement to use barrier contraceptive method (condom) and to continue its use for 6 months from receiving the last dose of 177Lu-PSMA-617. * Patient must have the ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: * Presence of a very high-risk feature: cT3b to T4 OR primary pattern 5 OR 2 to 3 high-risk features OR \>4 cores with Grade Group 4 or 5. * Any prior pharmacotherapy (with the exception of up to 45 days of ADT prior to randomization), radiation therapy, or surgery as treatment for prostate cancer. Any prior radiopharmaceutical therapy. * Any prior radiation to the pelvis. * Presence of N1 or M1 disease by conventional imaging (CT, MRI, and/or bone scan) or M1 disease by PSMA-PET (68Ga-PSMA-11 or 18F-DCFPyL). Lymph nodes with short axis \> 8 mm by CT will be considered N1 by conventional imaging. * Castration-resistant prostate cancer (CRPC). * Patient receiving any other investigational agents. * Patient is participating in a concurrent treatment protocol involving radiotherapy, surgery, or systemic anti-cancer agents. * Inadequate bone marrow reserve and organ function as detailed in 5.1.10. * Unable to lie flat during or tolerate PET/MRI, PET/CT or EBRT. * Concurrent serious medical condition that, in the opinion of the Investigator, would impair study participation. * Contraindication to receiving pelvic radiation, including history of or active inflammatory bowel disorders. * Refusal to sign informed consent.