East Maitland

The primary objective of the study is to compare radiographic progression-free survival (rPFS) in participants who receive 177Lu-TLX591 with SOC to rPFS in participants who receive SOC only. This study consists of three Parts: * Part 1: Safety and Dosimetry Lead-in, * Part 2: Randomized Treatment Expansion, and * Part 3: Long-term Follow-up The study will commence with a 30-patient safety and dosimetry lead-in (Part 1) and proceed to a randomization treatment expansion in approximately 490 patients (Part 2). Patients in Part 2 will be randomized in a 2:1 ratio to receive either 177Lu-TLX591 + Standard of Care SoC (Group A), or SoC alone (Arm B). SoC in this trial is either: ARPI (enzalutamide or abiraterone) or docetaxel. All patients will be followed in long-term follow-up for at least 5 years from the first therapeutic dose, death, or loss to follow up (Part 3). Only patients that meet PSMA-positivity criteria per Blinded Independent Central Review (BICR) will be eligible for this study.