Lu-PSMA and Stereotactic Radiotherapy Versus Radiotherapy Alone for Prostate Cancer (LUST) (LUST)

Inclusion Criteria: Patients must have 1-3 asymptomatic metastatic tumor(s) of the soft tissue or bone developed within the past 3-months that are ≤ 5.0 cm or < 250 cm3 documented at CT or Whole Body-Diffusion (WBD)-MRI. PSMA-PET/CT positive scan matching with lesions documented on baseline CT or WBD-MRI. Patients must have had their primary tumor treated with surgery and/or radiation and previous salvage radiation to the prostate bed or pelvis is allowed. Patients will be admitted to therapeutic phase only if the semi quantitative intensity of lesions uptake at the diagnostic PET/CT PSMA is higher than that of salivary glands or Standardized uptake value (SUV) has to be 1.5 times higher than the average total body. Histologic confirmation of malignancy (primary or metastatic tumor). Prostate specific antigen (PSA) ≥ 0.2 ng/mL but ≤ 50 ng/mL and Testosterone ≥ 125 ng/dL. PSA doubling time (PSADT) < 15 months. PSADT will be calculated using as many PSA values that are available from time of relapse (PSA > 0.2 ng/dL). Patients unfit or refusing ADT. Patients may have had prior systemic therapy and/or ADT associated with treatment of their primary prostate cancer. Patients may have had ADT associated with salvage radiation therapy. Patients must be ≥ 18 years of age. Patient understands the purpose of the study and the procedures required for it; the patient is willing to participate in the study and to sign a written informed consent document. Patients must have an Eastern Cooperative Oncology Group performance status ≤ 2. Patients should have a life expectancy of at least 6 months. Patients must have normal organ and marrow function. If the participant engages in sexual activity with a woman of childbearing potential, a condom must be used together with another highly effective method of contraception during the Treatment Period and for 3 months after the last dose of study intervention. The participant must agree not to donate sperm for the purpose of reproduction during the Treatment Phase and for a minimum of 3 months after receiving the last dose of study intervention. Highly effective birth control methods are required beginning at the screening visit and continuing until 6 months following last treatment with study drug. Patients and female partner who is of childbearing potential must use 2 acceptable methods of birth control (1 of which must include a condom as a barrier method of contraception, starting at screening and continuing throughout the study period and for 6 months after final study drug administration. Exclusion Criteria: No more than 3 years of ADT is allowed, with the most recent ADT treatment having occurred more than 6 months prior to enrollment. PSMA -PET/CT scan within the past 3 months with lesions not seen on baseline CT or WBD-MRI. Spinal cord compression or impending spinal cord compression. Suspected pulmonary and/or liver metastases. Bone metastasis in a femoral bone. Previous radiation therapy on the metastatic site. Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier. Participation in another clinical trial with any investigational agents within 30 days prior to study screening. Any condition for which, in the opinion of the investigator, participation would not be in the best interest of the participant. Patients with known brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. History of allergic reactions attributed to compounds of similar chemical or biologic composition to 177-Lu-PSMA- I&T or other agents used in the study. Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. Unable to lie flat during or tolerable SABR (Ablative stereotactic radiotherapy) Other known malignant neoplastic diseases in the patient's medical history with a disease-free interval of less than 5 years (except for previously treated basal cell carcinoma and in situ carcinoma of the uterine cervix); HIV-positivity, whether or not symptomatic.