This is a prospective, open-label, dose-escalation and randomized dose optimization and expansion study. The Phase Ib portion of the study aims to determine the safety and tolerability of escalating doses of [212Pb]Pb-ADVC001 administered every 6, 4, 2 or 1 week(s) and establish the recommended phase 2 doses (RP2D). The Phase 2a expansion aims to assess the efficacy and safety of [212Pb]Pb-ADVC001 at the RP2 doses in 3 participant groups.

Key Inclusion Criteria:

• Documented metastatic adenocarcinoma of the prostate, confirmed by histopathology.

• Progressive metastatic prostate cancer demonstrated by at least one of the following:

  1. Increase in PSA greater than 25% and > 2 ng/mL above nadir, confirmed by progression at two timepoints at least three weeks apart
  2. Progressive disease or new lesion(s) (relative to previous imaging) in the viscera or lymph nodes as per the Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 or in bone as per Prostate Cancer Clinical Trials Working Group 3 (PCWG3).

• For Phase 1b Dose Escalation: Metastatic castration-resistant prostate cancer (mCRPC) with exposure to at least one ARPi and taxane-based chemotherapy at any time in the course of their disease (unless taxanes considered contraindicated or declined by participant as documented in the patient's source documents and eCRF).

• For Phase 2a Dose Expansion:

  1. Group 1: Metastatic hormone-sensitive prostate cancer (mHSPC) with a sub-optimal PSA response defined as PSA ≥ 0.2 ng/mL despite receiving androgen deprivation therapy (ADT) and an androgen receptor pathway inhibitor (ARPi) without evidence of disease progression
  2. Group 2: Progressive mCRPC post ≥ 1 ARPi; 177Lutetium (177Lu)-PSMA-naïve and not previously treated with chemotherapy for CRPC
  3. Group 3: Progressive mCRPC with prior exposure to 177Lu-PSMA and ARPi

• Has disease that is prostate specific membrane antigen (PSMA) positive, as demonstrated by ⁶⁸Ga-PSMA-PET/CT or ¹⁸F-based PSMA PET/CT and confirmed as eligible by local reader. PSMA-positive participants are defined as those having at least one tumor lesion with ⁶⁸Ga- or ¹⁸F- PSMA PET CT uptake greater than normal liver (based on visual assessment) and all tumor lesions larger than size criteria with ⁶⁸Ga- or ¹⁸F-PSMA uptake greater than liver [short axis size criteria: organs ≥ 1 cm, lymph nodes ≥ 2.5 cm, bones (soft tissue component) ≥ 1 cm].

• Eastern Cooperative Oncology Group (ECOG) Performance Status 0 or 1.

• Adequate haematological, renal, and liver function.

Key Exclusion Criteria:

• Has received prior systemic radioligand therapy with the exception of prior radium-223. Prior 177Lu-PSMA is required for Phase 2a Group 3 participants.
• Systemic anti-cancer therapy and/or radiation therapy within four weeks of C1D1 or has received any investigational agent within four weeks of C1D1.
• Has malignancies other than prostate cancer within 3 years prior to enrolment, except for those with a negligible risk of metastases
• Known CNS metastases or symptoms of spinal cord compression or impending spinal cord compression. Patients with prior treatment for spinal cord compression should be clinically stable off steroids for at least 4 weeks.
• Has diffuse bone-marrow involvement, i.e, "superscan", defined as bone scintigraphy in which there is excessive skeletal radioisotope uptake.
• Has a serious active or sub-clinical infection, or angina pectoris, or heart failure (New York Heart Association [NYHA] Class III or IV), or significantly prolonged QT interval, or other serious illness which might impair the ability to participate in this study to the full extent, or which may require treatment that could interact with study treatment.
• Has a known alteration in breast cancer genes (BRCA) BRCA1 or BRCA2 and are eligible to receive poly ADP ribose polymerase (PARP) inhibitor therapy according to their treating institution's standard of care.