Personalized vs. Fixed-Activity 177Lu-PSMA-617 Radiopharmaceutical Therapy (PRODIGY-2)

Inclusion Criteria: 1. Patient aged ≥18 years with metastatic adenocarcinoma of the prostate, defined by documented histopathology of prostate adenocarcinoma; 2. Castration-resistant prostate cancer, as defined as disease progressing despite castration by orchiectomy or ongoing androgen deprivation therapy; 3. Progressive mCRPC with rising PSA level, defined by PCWG3 criteria (sequence of two rising values above a baseline at a minimum of 1-week intervals, with serum testosterone level ≤ 1.7 nmol/dL); 4. PSA ≥2 ng/mL ; 5. Prior treatment with at least one ARPI; 6. PSMA-expressing cancer, with significant PSMA expression defined as SUVpeak in at least one lesion that is superior to SUVmean of the liver on PSMA-PET (68Ga-PSMA-11 or 18F-DCFPyL), within 45 days prior to randomization; 7. ECOG Performance status 0 to 2; 8. Calculated eGFR (by CKD-EPI formula) ≥ 45 mL/min/1.73m\^2; 9. Albumin ≥ 25 g/L; 10. Platelets ≥ 100x10\^9/L; 11. Neutrophils ≥ 1.5x10\^9/L; 12. Hemoglobin ≥ 90 g/L without transfusion in the past 4 weeks; 13. Signed, written informed consent Exclusion Criteria: 1. PSMA-PET "superscan" (i.e. extensive/diffuse PSMA-positive bone involvement); 2. Site(s) of disease that are FDG-positive, defined as SUVpeak in at least one lesion that is superior to twice (2x) SUVmean of the liver, and PSMA-negative (as above), within 45 days prior to randomization; 3. Prior treatment with more than two lines of chemotherapy for mHSPC and/or mCRPC (adjuvant and neoadjuvant chemotherapy does not count) towards the maximum of two regimens); 4. Prior radiopharmaceutical therapy; 5. Known CNS metastasis unless they are deemed to be non-progressive, asymptomatic and off corticosteroid therapy for at least four weeks, as per investigator's assessment; 6. Active malignancy other than prostate cancer; 7. Patients who are sexually active and not willing/able to use medically acceptable forms of barrier contraception; 8. Any other condition, diagnosis or finding that may in the investigator's opinion interfere with trial conduct; 9. Known hypersensitivity to 177Lu-PSMA-617 or to any ingredient in the formulation, including any non-medicinal ingredient, or component of the container.