EValuation of radIOLigand Treatment in mEn With Metastatic Castration-resistant Prostate Cancer With [161Tb]Tb-PSMA-I&T

Inclusion Criteria: 1. Patient has provided written informed consent. 2. Male patients must be 18 years of age or older at the time of written informed consent. 3. Histologically or cytologically confirmed adenocarcinoma of the prostate, OR unequivocal diagnosis of metastatic prostate cancer (i.e., involving bone or pelvic lymph nodes or para-aortic lymph nodes) with an elevated serum prostate specific antigen (PSA). 4. Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2. 5. Patients must have had prior treatment with at least one line of taxane chemotherapy, unless medically unsuitable. 6. Patients must have had prior treatment with at least one second-generation androgen receptor (AR)-targeted agent (e.g., enzalutamide, abiraterone, apalutamide or darolutamide). 7. Patients must have progressive disease defined according to The Prostate Cancer Clinical Trials Working Group 3 (PCWG3) as any one of the following: 1. PSA progression - minimum of 2 rising PSA values from a baseline measurement with an interval of ≥ 1 week between each measurement 2. Soft tissue progression as per Response Evaluation Criteria in Solid Tumours version 1.1 (RECIST 1.1) criteria 3. Bone progression: ≥ 2 new lesions on bone scan 8. Prior surgical orchiectomy or chemical castration maintained on luteinizing hormone-releasing hormone (LHRH) analogue (agonist or antagonist). 9. Serum testosterone levels ≤ 1.75nmol/L (≤ 50ng/dL). 10. Significant prostate specific membrane antigen (PSMA) avidity on PSMA positron emission tomography (PET)/computed tomography (CT), defined as a minimum uptake of maximum standardised uptake value (SUVmax) 20 at a site of disease, and SUVmax \> 10 at sites of measurable soft tissue disease ≥ 15mm (unless subject to factors explaining a lower uptake, e.g. respiratory motion, reconstruction artefact). 11. Patients must have a life expectancy ≥ 6 months. 12. Patients must have adequate bone marrow, hepatic and renal function, defined as: 1. Haemoglobin ≥ 100g/L independent of transfusions (no red blood cell transfusion in last 4 weeks) 2. Absolute neutrophil count (ANC) ≥ 1.5 x 10\^9/L 3. Platelets ≥ 150 x 10\^9/L 4. Total bilirubin ≤ 1.5x upper limit of normal (ULN) except for patients with known Gilbert's syndrome, where this applies for the unconjugated bilirubin component 5. Aspartate transaminase (AST) and alanine transaminase (ALT) ≤ 3x ULN if there is no evidence of liver metastasis or ≤ 5x ULN in the presence of liver metastases 6. Adequate renal function: patients must have a creatinine clearance estimated of ≥ 40mL/min using the Cockcroft Gault equation (Appendix 3) 13. Sexually active patients are willing to use medically acceptable forms of barrier contraception. 14. Willing and able to comply with all study requirements, including all treatments and the timing and nature of all required assessments. 15. At least 3 weeks since the completion of surgery or radiotherapy prior to registration. Exclusion Criteria: 1. Prior treatment with another radioisotope (i.e. PSMA radioligands, radium-223, strontium-89, samarium-153). 2. Site(s) of discordant disease on PET imaging (Fluorodeoxyglucose \[FDG\]-positive and minimal PSMA-uptake). 3. Other malignancies (in addition to the prostate cancer being treated on this study) within the previous 2-years prior to registration other than basal cell or squamous cell carcinomas of skin or other cancers that are unlikely to recur within 24 months. 4. Symptomatic brain metastases or leptomeningeal metastases. 5. Patients with symptomatic or impending cord compression unless appropriately treated beforehand and clinically stable for more than 4 weeks. 6. Concurrent illness, including severe infection that may jeopardize the ability of the patient to undergo the procedures outlined in this protocol with reasonable safety.