STereotActic Body Radiotherapy and 177Lutetium PSMA in Locally Advanced Prostate Cancer

Inclusion Criteria: * Participant must be ≥ 18 years of age. * ECOG performance status ≤ 1 * Histologic confirmation of prostate adenocarcinoma of the prostate * PSMA avid disease on PSMA PET/CT, where the tumor in the prostate has SUVmax ≥ 10. * PSMA PET/CT must be obtained within 4 months. * Need ≥ 1 criteria: * Node positive disease on PSMA PET/CT or conventional imaging, as defined by having any of the following: * Pelvic nodal disease (cN1) as defined by LN stations that commence at the bifurcation of the common iliac vessels * Regional nodal disease (M1a) as defined by LN stations that commence at the bifurcation of the aorta and bifurcation of the proximal inferior vena cava to the common iliac veins. * In the absence of nodal metastasis, must have ≥ 2 of the following * i. cT3a or cT3b by conventional imaging (MRI) or PSMA PET/CT * ii. Grade group ≥ 4 * iii. PSA ≥ 40 ng/mL * Adequate organ and marrow function to receive treatment: * Hemoglobin \> 10 g/dL * White blood cell (WBC) \> 3000 / mL * Absolute neutrophil count ≥ 1,500 / mcL * Platelets ≥ 100,000 / mcL * Creatinine ≤ 1.5x ULN * Estimated glomerular filtration rate (eGFR)\* \> 50 mL/min * Total bilirubin\*\* \< 2× ULN * Albumin \> 3 g/dL * Aspartate aminotransferase (AST) \< 3× ULN * \*based upon Chronic Kidney Disease- Epidemiology Collaboration (CKD-EPI) equation. Participants with estimated GFR between 50 - 60 mL/min will require a 99mTc-TPA GFR test and only participants with non-obstructive pathology will be included in the study. * \*\* Total bilirubin ≤ 2x ULN (except for participants with known Gilbert's Syndrome ≤ 3x ULN is permitted) * International Prostate Symptoms Score (IPSS) ≤ 15. * Medically fit for treatment and agreeable to follow-up. * Ability to understand and the willingness to sign a written informed consent. * Participants with partners of childbearing potential, agreement to use barrier contraceptive method (condom) and to continue its use for 14 weeks from receiving the last dose of Lu-PSMA-617. Participants must also not donate sperm for 14 weeks from receiving the last dose of Lu-PSMA-617. Exclusion Criteria: * Clinical or radiographic evidence of distant metastatic disease (M1a above aortic bifurcation, M1b, or M1c) by any imaging. Participants are allowed to M1a nodal disease that is below the aortic bifurcation. Negative PSMA PET/CT is an acceptable substitute to conventional staging. * Prostate gland size \>90 cc measured by CT, ultrasound, or MRI * Prior head and neck radiation therapy. * Prior treatment for prostate cancer (incudes chemotherapy, radiation therapy, or anti-androgen therapy). * Prohibited within 30 days prior to administration to study treatment: spironolactone and other investigational drug therapies. * Prohibited 3 months before participant registration and during administration of study treatment: oral ketoconazole, , estrogens, and radiopharmaceuticals. * History of prior pelvic radiation therapy. * Enrollment concurrently in another investigational drug study within 6 months of registration. * History of another active malignancy within the previous 3 years except for adequately treated skin cancer or superficial bladder cancer. * History of prior myelodysplastic syndrome or acute leukemia. * History of or active Crohn's disease or ulcerative colitis. * Contraindication to or inability to tolerate PSMA/PET. * Any condition that in the opinion of the investigator would preclude participation in this study. * Inability to adhere to radiation safety measures in hospital or at home * Prior treatment with radionuclide therapies, 177Lu-PSMA-617 or other * Reduced salivary gland function with baseline CTCAE Gr \> 1 dry mouth will be excluded.