• The patient must have a biopsy proven adenocarcinoma of the prostate (biopsy confirmation of the primary tumor or oligometastatic tumor is acceptable)

• The patient's primary tumor must have been previously treated with surgery and/or definitive radiation. Prior salvage treatments (radiation or surgery) to the prostate bed or pelvis is allowed.

• Patients must have a negative multiparametric MRI and/or negative biopsy of the prostate (or prostate bed) even if other imaging modality (including PSMA) was negative for disease in the prostate (or prostate bed) within 2 months of enrollment on study

• Patients must have had a PSMA scan within 2 months of enrollment on study

• Patient has not received any form of prostate-cancer directed therapy since undergoing screening PSMA scan

• Patient must have 1-5 oligometastatic tumors or lesions of the bone or soft tissue that are detectable on a PSMA PET scan.

‣ Outside PSMA scans not performed at MSKCC are acceptable but will require official read by MSKCC nuclear medicine for confirmation of metastasis

⁃ Patients with sclerotic, non-PSMA avid osseous lesions which are not felt to reflect active metastatic disease by a radiologist are eligible for the protocol assuming they also have 1-5sites of PSMA avid disease as well as no non-PSMA avid sites which are felt to reflect active metastatic prostate cancer

• All oligometastatic lesions must be amenable to SBRT to a dose of 9 Gy x 3 without exceeding nationally recognized dose limits to adjacent organs at risk as deemed by the treating radiation oncologist

• Patient's insurance is willing to cover SBRT treatment or the patient agrees to cover the costs of this therapy

• Patient must have a prostate specific antigen (PSA) ≥ 0.2 ng/mL but ≤ 50 ng/mL

• Patient may have had prior systemic therapy and/or ADT associated with treatment of their primary prostate cancer. Patient may have had ADT associated with salvage radiation therapy.

‣ Patients who have been on hormone therapy within 12 months of consent must have testosterone within normal range (221-716 ng/dL at MSKCC) in order to be eligible for treatment on study.

⁃ Baseline testosterone below the normal range for patients who have not had hormone therapy within 12 months of study entry is acceptable

• Patient must have an Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2

• Patient must have a serum creatinine level \< 1.5 x ULN or EGFR \> 60 mL/min

• Patient must have adequate liver laboratory values:

‣ ALT and AST ≤ 2.5 x ULN

⁃ Albumin \> 2 g/ dL

⁃ Bilirubin \< 3 X ULN

• Patient must have normal organ and marrow function as defined as:

‣ Total white blood count \> 3.0 K/mcL

⁃ Absolute Neutrophil Count ≥ 1.5 K/mcL

⁃ Platelets ≥ 100 K/mcL

⁃ Hemoglobin ≥ 9 g/dL

• The effects of 177Lu-PSMA-617 and SBRT on the developing human fetus at the recommended therapeutic dose are unknown. Men (including men with vasectomies) must agree to use adequate contraception (a condom and another effective method of birth control) prior to registration, for the duration of study participation, and for at least 3 months thereafter. Men must also agree not to donate sperm for the duration of study participation, and for at least 3 months thereafter.

• Patient must be ≥ 18 years of age

• Ability to understand, and willingness to sign the informed consent