Key Inclusion Criteria:

• Signed informed consent must be obtained prior to participation in the study.

• Participants must be adults ≥ 18 years of age.

• Participants must have an ECOG performance status of 0 to 2.

• Participants must have histologically confirmed adenocarcinoma of the prostate. Participants with other histology (e.g. neuroendocrine, intraductal subtype) are not eligible.

• Phase Ib: Prior exposure of up to 1 line of taxane-based chemotherapy is permissible. Phase II: Participants must not have received taxane-based chemotherapy in mCRPC setting (allowed in mHSPC setting).

• Participants must have PSMA-PET positive disease assessed by using a PSMA imaging agent that is approved as per protocol and are eligible as determined by the sponsor's central reading rules.

• Castration level of testosterone (< 50 ng/dL), and/or use of concomitant ADT

• Participant must have been diagnosed with mCRPC with documented progressive disease while on treatment with ARPI in mHSPC or earlier setting as their last treatment (and did not progress on more than one ARPI), based on at least 1 of the following criteria:

  • Serum/plasma PSA progression is defined as 2 increases in PSA measured at least 1 week apart. The minimal start value is 2.0 ng/mL; 1.0 ng/mL is the minimal starting value if confirmed rise in PSA is the only indication of progression as per PCWG3 guidelines.
  • Soft-tissue progression defined PCWG3-modified RECIST v1.1 (Eisenhauer et al 2009, Scher et al 2016).
  • Progression of bone disease: 2 new lesions; only positivity on the bone scan defines metastatic disease to bone (PCWG3 criteria Scher et al 2016).

Key Exclusion Criteria:

• Concurrent local (radiation therapy to the prostate with curative intent or other prostate antineoplastic ablative procedures) or systemic (hormonal ablation, chemotherapy, immunotherapy, , RLTs) antineoplastic treatments, or within 28 days of enrollment (Phase Ib) or randomization (Phase II)
• Prior treatment with any RLT or PSMA-targeted agents (approved or investigational)
• Any other investigational agents within 28 days prior to first dose of any study treatment
• Concurrent serious medical conditions that may interfere with study procedures or followup
• Participants with a history of CNS metastases must have received therapy (surgery, whole brain radiation therapy, stereotactic radiosurgery) and be neurologically stable, asymptomatic, and not taking corticosteroids for the purpose of maintaining neurologic integrity.

Other protocol-defined inclusion/exclusion criteria may apply.