Combination of Radium-223 and Lutetium-177 PSMA-I&T in Men with Metastatic Castration-Resistant Prostate Cancer

Inclusion Criteria: * Patient must be ≥ 18 years of age and must have provided written informed consent. * 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 PSA. * Eastern Cooperative Oncology Group (ECOG) performance status of ≤ 2 * Patients must have progressed on ≥ 1 second-generation AR-targeted agent (e.g., enzalutamide, abiraterone, apalutamide, or darolutamide). * Patients must have progressive disease for study entry. PCWG3 defines this as any one of the following: * PSA progression: minimum of two rising PSA values from a baseline measurement with an interval of ≥ 1 week between each measurement. * Soft tissue progression as per RECIST 1.1 criteria * Bone progression: ≥ 2 new lesions on bone scan * Symptomatic progression eg. Bone pain * At least three weeks since receiving anti-cancer treatment (other than ADT), the completion of surgery or radiotherapy prior to registration. * Prior surgical orchiectomy or chemical castration maintained on luteinizing hormone-releasing hormone (LHRH) analogue (agonist or antagonist). * Serum testosterone levels ≤ 1.75nmol/L (≤ 50ng/dL) within 28 days before registration. * Significant PSMA avidity on PSMA PET/CT, defined as a minimum uptake of SUVmax 20 at a site of disease, and SUVmax \>10 at sites of measurable disease \>10mm (unless subject to factors explaining a lower uptake, e.g. respiratory motion, reconstruction artefact). * ≥ 2 bone metastases must be present on bone scintigraphy which have not been previously treated with radiotherapy. * No contraindication to treatment with a bone antiresorptive agent such as denosumab or zoledronic acid. * Patients must have adequate bone marrow, hepatic and renal function documented within 28 days prior to registration, defined as: * Haemoglobin ≥ 90 g/L independent of transfusions (no red blood cell transfusion in last four weeks) * Absolute neutrophil count ≥ 1.5x10\^9/L * Platelets ≥ 150 x10\^9/L * Total bilirubin ≤ 1.5 x upper limit of normal (ULN) except for patients with known Gilbert's syndrome, where this applies for the unconjugated bilirubin component. * Aspartate transaminase (AST) and alanine transaminase (ALT) ≤ 2.5 x ULN if there is no evidence of liver metastasis or ≤ 5 x ULN in the presence of liver metastases * Albumin ≥ 25 g/L * Adequate renal function: patients must have a creatinine clearance estimated of ≥ 40 mL/min using the Cockcroft Gault equation * Sexually active patients are willing to use medically acceptable forms of barrier contraception. * Willing to undergo biopsies, if disease is considered accessible and biopsy is feasible. * Willing and able to comply with all study requirements, including all treatments and the timing and nature of all required assessments. Exclusion Criteria: Patients who meet any of the following criteria will be excluded from study entry: * Superscan on Bone scan (WBBS) or diffuse marrow involvement on PSMA PET/CT * Prior treatment with 223Ra or 177Lu-PSMA. * Has received more than one previous line of chemotherapy for the treatment of metastatic prostate cancer. * Sites of discordant FDG-positive disease defined by minimal PSMA-expression and no uptake on WBBS (for bone metastases). * Other malignancies within the previous 2 years other than basal cell or squamous cell carcinomas of skin or other cancers that are unlikely to recur within 24 months. * Symptomatic brain metastases or leptomeningeal metastases. * Patients with symptomatic or impending cord compression unless appropriately treated beforehand and clinically stable for ≥ four weeks. * Concurrent illness, including severe infection that may jeopardise the ability of the patient to undergo the procedures outlined in this protocol with reasonable safety.