A Study of Stereotactic Body Radiotherapy and 177Lu-PSMA-617 for the Treatment of Prostate Cancer

Inclusion Criteria: * 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 °If patient is post-prostatectomy, the MRI Prostate can be excluded at clinician's discretion * 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 ol…