External Beam Therapy With Theranostic Radioligand Therapy for Oligometastatic Prostate Cancer (ProstACT TARGET)

Inclusion Criteria: * Signed Informed Consent Form * Male, aged ≥ 18 years * Estimated life expectancy of at least 6 months * Eastern Cooperative Oncology Group (ECOG) score 0 - 2 * Biopsy proven prostate adenocarcinoma with Gleason Score 7 or more at primary presentation * Previous Radical Prostatectomy (RP) with curative intent (+/- post-operative radiotherapy to prostate bed) * Biochemical relapse, as defined by EAU-ESTRO-SIOG Guidelines (serum PSA \> 0.2 ng/mL, confirmed by repeat measurements) * PSMA-ligand avid pelvic nodal disease on PSMA-ligand PET/CT, with visualised disease confined to the pelvis with or without evidence of PSMA-avid disease in the prostate bed * At least one pelvic nodal lesion ≥ 5 mm in the greatest dimension. SUVmax \> 9 in enlarged nodes; SUVmax \> 3 in nodes 5 mm or less * Oligometastatic disease as defined by ≤ 5 metastatic lymph nodes * Metastatic lymph nodes not beyond the aortic bifurcation * Non-castrate levels of testosterone (\> 20 ng/dL) * Chemotherapy naïve * Adequate renal function: Cr Cl ≥ 40 mL/min (determined by Cockcroft-Gault formula) * Adequate bone marrow function: Hb \> 90 g/L; platelets \> 100 x 109/L; neutrophils \> 1.5 x 109/L * Adequate liver function: bilirubin \< 1.5 x upper limit of normal (ULN); AST, ALT, ALP \< 2 x ULN; albumin \> 30 g/L * Willing and able to comply with all trial requirements, including all treatments and pre- and post-treatment assessments * Able to commence treatment within 28 days of enrolment Exclusion Criteria: * Previous external beam radiotherapy to pelvis for other malignancies or medical conditions (except for post-operative prostate bed radiotherapy for prostate cancer) * Androgen deprivation therapy within 12 months of trial screening * Known androgen deficiency * Bone or visceral metastases * Lymph node metastases above the aortic bifurcation * Contraindications to pelvic irradiation as determined by Investigator (e.g., chronic inflammatory bowel disease) * At increased risk of haemorrhage, or recent history of a thrombotic event (e.g., Deep Vein Thrombosis \[DVT\]/Pulmonary Embolism \[PE\]) and/or are using long-term anti-coagulant or anti-platelet agents) * Known hypersensitivity to any isotope of lutetium (Lu) in any chemical form, or any isotope used in PSMA imaging * Contraindication to intravenous contrast * Evidence of urinary tract stricture, or significant urinary/faecal incontinence Presence of active infection at time of screening, or history of serious infection within the previous 4 weeks * History of any malignancy other than prostate cancer within 5 years of enrolment (excluding localised non-melanoma skin cancers) * Any uncontrolled significant medical, psychiatric, or surgical condition (e.g., active infection, unstable angina pectoris, cardiac arrhythmia, poorly controlled type 2 diabetes, uncontrolled congestive heart failure, pulmonary disease), or laboratory findings that, in the opinion of the Investigator, may jeopardise the participant's safety or that would limit compliance with the treatment and assessment requirements of the trial * Any cognitive impairment or other condition that may render the participant unable to adequately understand the requirements, nature, and possible consequences of the trial. * Intention to father children within a timeframe corresponding with the duration of the allocated treatment regime plus 12 weeks.