Inclusion Criteria:  Signing informed consent Adenocarcinoma of Prostate proven by histopathology Life expectancy of 6 months or more Unresectable metastases Progressive disease, with docetaxel/cabazitaxel or declined taxane therapy by the patient 177Lu-PSMA-617 naive or 177Lu-PSMA-617/177Lu-PSMA-I&T treated If BRCA mutations or microsatellite instability is present, patients should have received FDA approved therapies such as PARP inhibitors and pembrolizumab, and progressed Castration-resistant disease with confirmed testosterone level ≤50 ng/ml under prior androgen deprivation therapy (ADT) Positive 68Ga-PSMA-11 PET/CT for the majority of measurable diseases defined as SUV ≥2.0 ECOG 0-2 Hemoglobin concentration ≥ 9.0 g/dL Platelet counts ≥100 × 109/L White blood cell count ≥ 2.0 × 109/L), ANC>1.5 x109/L Glomerular Filtration Rate (GFR) ≥ 60 ml/min AST and ALT ≤ 5xULN Billirubin ≤ 3x ULN Albumin ≥ 25 g/L Serum/plasma creatinine ≤1.5 × ULN or creatinine clearance ≥50 mL/min based on Cockcroft-Gault formula Received at least one ARAT in the past Patients on anti-androgen therapy are allowed to continue their treatment at the discretion of their oncologists  Exclusion Criteria:  Inclusion Criteria: Signing informed consent. Adenocarcinoma of Prostate proven by histopathology Life expectancy of 6 months or more. Unresectable metastases. Progressive disease, with docetaxel/cabazitaxel or declined taxane therapy by the patient. 177Lu-PSMA-617 naive or 177Lu-PSMA-617/177Lu-PSMA-I&T treated. If BRCA mutations or microsatellite instability is present, patients should have received FDA approved therapies such as PARP inhibitors and pembrolizumab, and progressed Castration resistant disease with confirmed testosterone level ≤50 ng/mlunder prior androgen deprivation therapy (ADT) Positive 68Ga-PSMA-11 PET/CT for the majority of measurable disease defined as SUV ≥2.0. ECOG 0-2 Hemoglobin concentration ≥ 9.0 g/dL Platelet counts ≥100 × 109/L White blood cell count ≥ 2.0 × 109/L), ANC>1.5 x109/L Glomerular Filtration Rate (GFR) ≥ 60 ml/min AST and ALT ≤ 5xULN Billirubin ≤ 3x ULN Albumin ≥ 25 g/L. Serum/plasma creatinine ≤1.5 × ULN or creatinine clearance ≥50 mL/min based on Cockcroft-Gault formula Received at least one ARAT in the past. Patients on anti-androgen therapy are allowed to continue their treatment at the discretion of their oncologists.  Exclusion Criteria:  Less than 6 weeks since last myelosuppressive therapy (including Docetaxel, Cabazitaxel, 223Ra, 153Sm, 177Lu-PSMA-617, 177Lu-PSMA-I&T) or other radionuclide therapy permitted (including 223Ra, 153Sm) Urinary tract obstruction as evidenced by Tc-99m DTPA renal scan with diuretics Abnormal renal function (eGFR <60 mL/min), baseline Hgb <9g/dL, ANC<1.5 x109/L, platelets <100 x109/L, and PT, INR or PTT ≥1.5xULN Persistent baseline dry eye or dry mouth from prior RLT Persistent prior AEs >Grade 1 from prior anti-cancer therapies Administration of an investigational agent ≤60 days or 5 half-lives, whichever is shorter, prior to randomization The known presence of central nervous system metastases Active malignancy other than low-grade non-muscle-invasive bladder cancer and non-melanoma skin cancer Concurrent illness that may jeopardize the patient's ability to undergo study procedures. Symptomatic cord compression, or clinical or radiologic findings indicative of impending cord compression Concurrent serious (as determined by the investigator) medical conditions, including, but not limited to, New York Heart Association class III or IV congestive heart failure Major surgery ≤30 days prior to randomization Planning to conceive pregnancy during the treatment and up to 6 months after the last treatment