Study Evaluating mCRPC Treatment Using PSMA [Lu-177]-PNT2002 Therapy After Second-line Hormonal Treatment

Inclusion Criteria: 1. Male aged 18 years or older. 2. Histological, pathological, and/or cytological confirmation of adenocarcinoma of the prostate. 3. Ineligible or averse to chemotherapeutic treatment options. 4. Patients must have progressive mCRPC at the time of consent based on at least 1 of the following criteria: 1. Serum/plasma PSA progression defined as increase in PSA greater than 25% and \>2 ng/mL above nadir, confirmed by progression at 2 time points at least 3 weeks apart. 2. Soft-tissue progression defined as an increase ≥20% in the sum of the diameter (SOD) (short axis for nodal lesions and long axis for non-nodal lesions) of all target lesions based on the smallest SOD since treatment started or the appearance of one or a new lesion. 3. Progression of bone disease defined as the appearance of two or more new lesions by bone scan. 5. Progression on previous treatment with one ARAT (abiraterone or enzalutamide or darolutamide or apalutamide) in either the CSPC or CRPC setting. 6. PSMA-PET scan (i.e., 68Ga-PSMA-11 or 18F-DCFPyL) positive as determined by the sponsor's central reader. 7. Castrate circulating testosterone levels (\<1.7 nmol/L or \<50 ng/dL). 8. Adequate organ function, independent of transfusion: 1. Bone marrow reserve: * i. White blood cell (WBC) count ≥2.5 × 10\^9/L OR absolute neutrophil count (ANC) ≥1.5 × 10\^9/L. * ii. Platelets ≥100 × 10\^9/L. * iii. Hemoglobin ≥8 mmol/L. 2. Liver function: * i. Total bilirubin ≤1.5 × institutional upper limit of normal (ULN). For patients with known Gilbert's syndrome, ≤3 × ULN is permitted. * ii. ALT or AST ≤3.0× ULN. 3. Renal function: * i. Serum/plasma creatinine ≤1.5 × ULN or creatinine clearance ≥50 mL/min based on Cockcroft-Gault formula (for patients in France, serum/plasma creatinine ≤1.5 × ULN or CrCl ≥60 mL/min based on Cockcroft-Gault formula). 4. Albumin ≥30 g/L. 9. Human immunodeficiency virus-infected patients who are healthy and have a low risk of acquired immunodeficiency syndrome-related outcomes are included in this trial. 10. For patients who have partners who are pregnant or of childbearing potential: a condom is required along with a highly effective contraceptive method during the study and for 6 months after last study drug administration. Such methods deemed highly effective include a) combined (estrogen and progestogen containing) hormonal contraception associated with inhibition of ovulation, b) progestogen-only hormonal contraception associated with inhibition of ovulation, c) intrauterine device (IUD), d) intrauterine hormone-releasing system (IUS), e) bilateral tubal occlusion, f) vasectomy, g) true sexual abstinence: when this is in line with the preferred and usual lifestyle of the subject \[periodic abstinence (e.g., calendar, ovulation, symptothermal, post-ovulation methods), declaration of abstinence for the duration of exposure to IMP, and withdrawal are not acceptable methods of abstinence\]. 11. Willing to initiate ARAT therapy (either enzalutamide or abiraterone), pre-specified by investigator, if randomized to Treatment Arm B. 12. ECOG performance status 0 to 1. 13. Willing and able to comply with all study requirements and treatments (including 177Lu PNT2002) as well as the timing and nature of required assessments. 14. Signed informed consent. Exclusion Criteria: Patients are excluded from the study if any of the following criteria apply: 1. If noted in pathology report, prostate cancer with known significant (\>10% present in cells) sarcomatoid or spindle cell or neuroendocrine components. Any small cell component in the cancer should result in exclusion. 2. Prior treatment for prostate cancer ≤28 days prior to randomization, with the exclusion of first-line local external beam, ARAT, luteinizing hormone-releasing hormone (LHRH) therapy, or non-radioactive bone-targeted agents. 3. Any prior cytotoxic chemotherapy for CRPC (e.g., cabazitaxel or docetaxel); chemotherapy for hormone-sensitive prostate cancer (HSPC) is allowed if the last dose was administered \>1 year prior to consent. 4. Prior treatment with systemic radionuclides (e.g. radium-223, rhenium-186, strontium 89). 5. Prior immuno-therapy, except for sipuleucel-T. 6. Prior PSMA-targeted radioligand therapy, e.g., Lu-177-PSMA-617, I 131-1095. 7. Prior poly ADP ribose polymerase (PARP) inhibitor for prostate cancer. 8. Patients who progressed on 2 or more lines of ARATs. 9. Patients receiving bone-targeted therapy (e.g. denosumab, zoledronic acid) not on stable doses for at least 4 weeks prior to randomization. 10. Administration of an investigational agent ≤60 days or 5 half-lives, whichever is shorter, prior to randomization. 11. Major surgery ≤30 days prior to randomization. 12. Estimated life expectancy \<6 months as assessed by the principal investigator. 13. Presence of liver metastases \>1 cm on abdominal imaging. 14. A superscan on bone scan defined as a bone scan that demonstrates markedly increased skeletal radioisotope uptake relative to soft tissues in association with absent or faint genitourinary tract activity. 15. Dose escalation or initiation of opioids for cancer-related pain ≤30 days prior to consent up to and including randomization. 16. Known presence of central nervous system metastases. 17. Contraindications to the use of planned ARAT therapy, \[Ga-68\]-PSMA-11, \[F-18\]-DCFPyL or \[Lu-177\]-PNT2002 therapy, including but not limited to the following: * Hypersensitivity to \[Ga-68\]-PSMA-11, \[F-18\]-DCFPyL or \[Lu-177\]-PNT2002 excipients (Diethylenetriaminepentaacetic acid (DTPA), Sodium ascorbate, Lascorbic acid, Sodium gentisate, HCl, Sodium hydroxide). * Recent myocardial infarction or arterial thrombotic events (in the past 6 months) or unstable angina (in the past 3 months), bradycardia or left ventricular ejection fraction measurement of \< 50%. * History of seizures in patients planned to receive enzalutamide. 18. Active malignancy other than low-grade non-muscle-invasive bladder cancer and non-melanoma skin cancer. 19. Concurrent illness that may jeopardize the patient's ability to undergo study procedures. 20. Serious psychological, familial, sociological, or geographical condition that might hamper compliance with the study protocol and follow-up schedule. Patients that travel need to be capable of repeated visits even if they are on the control arm. 21. Symptomatic cord compression, or clinical or radiologic findings indicative of impending cord compression. 22. Concurrent serious (as determined by the investigator) medical conditions, including, but not limited to, New York Heart Association class III or IV congestive heart failure (see 12.1 Appendix 1), unstable ischemia, uncontrolled symptomatic arrhythmia, history of congenital prolonged QT syndrome, uncontrolled infection, known active hepatitis B or C, or other significant co-morbid conditions that in the opinion of the investigator would impair study participation or cooperation.