Study to Evaluate the Efficacy and Safety of 177Lu-NYM032 Injection in Participants With Progressive, PSMA-Positive Metastatic Castration-Resistant Prostate Cancer (mCRPC)

Inclusion Criteria: 1. Patient must be male and aged ≥18 years old. 2. Patients must have histological, pathological, and/or cytological confirmation of prostate cancer. 3. Patient's serum/plasma testosterone level must be at a castrate level (\<50 ng/dL or \<1.7 nmol/L). 4. Participants must have ≥1 metastatic lesion that is present on baseline CT, MRI, or bone scan imaging obtained ≤ 28 days prior to randomization. 5. Patients must have progressive mCRPC. Documented progressive mCRPC will be based on at least 1 of the following criteria: * Serum PSA progression defined as 2 consecutive increases in PSA over a previous reference value measured at least 1 week prior. The minimal start value is 2.0 ng/mL. * Soft-tissue progression defined \[PCWG3-modified RECIST v1.1 (Eisenhauer et al 2009, Scher et al 2016)\] * Progression of bone disease: appearance of 2 or more new bone lesions on bone scan (PCWG3 criteria (Scher et al 2016)) 6. Patients must have a positive 68Ga-NYM032 PET/CT scan. 7. Patients must have an ECOG performance status of 0 to 2. 8. Patients must have a life expectancy ≥ 6 months. 9. Participants must have been previously treated with at least 1 novel androgen receptor pathway inhibitor (ARPI) (e.g., abiraterone and/or enzalutamide) and at least 1, but no more than 2, previous taxane-based chemotherapy regimens. A taxane-based chemotherapy regimen is defined as a minimum exposure of 2 cycles of a taxane. If a participant has received only 1 taxane-based chemotherapy regimen, the participant is eligible : if the participant is unwilling to receive a second taxane-based chemotherapy regimen or if the participant's physician deems the participant unsuitable to receive a second taxane-based chemotherapy regimen (e.g., frailty assessed by geriatric or health status evaluation, intolerance, etc.). 10. Patients must have adequate organ function: 1. Bone marrow reserve: * White blood cell (WBC) count ≥2.5 x 109/L * Hemoglobin≥ 10.0 g/dL (9 g/dL is equivalent to 90 g/L and 5.59 mmol/L) * Absolute neutrophil count (ANC) ≥1.5 x 10\^9/L (1.5 x 10\^9/L is equivalent to 1.5 x 10\^3/µL and 1.5 x K/µL and 1.5 x 10\^3/cumm and 1500/µL) * Platelets≥ 100 x 10\^9/L (100 x 10\^9/L is equivalent to 100 x 10\^3/µL and 100 x K/µL and 100 x 10\^3/cumm and 100,000/µL) 2. Hepatic: * Total bilirubin ≤1.5 x the institutional upper limit of normal (ULN). For patients with known Gilbert's Syndrome ≤ 3 x ULN is permitted * Alanine aminotransferase (ALT) or aspartate aminotransferase (AST) ≤3.0 x ULN OR ≤5.0 x ULN for patients with liver metastases 3. Renal: * Serum creatinine ≤1.5 x ULN and creatinine clearance ≥50 mL/min * Albumin \>3.0 g/dL (3.0 g/dL is equivalent to 30 g/L) 11. For patients who have partners of childbearing potential:Partner and/or patient must use a method of birth control with adequate barrier protection, deemed acceptable by the principle investigator during the study and for 6 months after last study drug administration. Patients must not donate sperm during this period. 12. Patients must have the ability to understand and sign an approved ICF. Exclusion Criteria: 1. Any systemic anti-cancer therapy (e.g. chemotherapy, immunotherapy or biological therapy \[including monoclonal antibodies\], excluding ARPI therapy;) anticancer device therapy, radiation therapy, or an investigational drug in a clinical study within 4 weeks prior to day of randomization. 2. Previous treatment with any of the following within 6 months of randomization: Strontium-89, Samarium-153, Rhenium-186, Rhenium-188, Radium-223, hemi-body irradiation. 3. Previous PSMA-targeted radioligand therapy is not allowed. 4. Patients with a history of Central Nervous System (CNS) metastases must have received therapy (surgery, radiotherapy, gamma knife) and be neurologically stable, asymptomatic, and not receiving corticosteroids for the purposes of maintaining neurologic integrity. Patients with epidural disease, canal disease and prior cord involvement are eligible if those areas have been treated, are stable, and not neurologically impaired. 5. Symptomatic cord compression, or clinical or radiologic findings indicative of impending cord compression. 6. Any disease involving the cardiac, respiratory, renal, hepatic, or hematologic organ systems that would significantly interfere with completion of the study or confound the determination of the causality of any adverse events in the study. 7. Severe urinary incontinence, hydronephrosis, severe voiding dysfunction, or other related conditions. Note: Participants with bladder outlet obstruction or urinary incontinence that can be managed with available best standard of care (including urinary pads, drainage, etc.) are eligible for study participation. 8. Any toxicity related to prior anti-cancer therapies that has not recovered to ≤ Grade 2 according to NCI CTCAE v6.0, except for alopecia. 9. Uncontrolled or clinically significant cardiovascular disease, including but not limited to: * History of symptomatic congestive heart failure (New York Heart Association \[NYHA\] Class III to IV) or any arterial thromboembolic events (e.g., myocardial infarction, unstable angina, cerebrovascular accident, or transient ischemic attack) within 6 months prior to randomization; * Uncontrolled hypertension, defined as systolic blood pressure (SBP) ≥160 mmHg and/or diastolic blood pressure (DBP) ≥100 mmHg despite antihypertensive therapy; * Serious cardiac arrhythmias requiring treatment; * Prolonged corrected QT interval using Fridericia' s formula (QTcF) \>450 ms (male). 10. Clinically significant concomitant pulmonary diseases, including but not limited to: * History of interstitial lung disease (ILD)/interstitial pneumonia requiring steroid treatment (non-infectious), current ILD/interstitial pneumonia, or suspected ILD/interstitial pneumonia that cannot be ruled out by imaging assessment; * Pulmonary embolism within 3 months prior to randomization; * Any documented autoimmune, connective tissue, or inflammatory disease at screening (e.g., rheumatoid arthritis, Sjögren's syndrome, sarcoidosis) with suspected pulmonary involvement; * Prior pneumonectomy; * Other moderate to severe pulmonary diseases that significantly impair respiratory function and may interfere with the detection or management of drug-related pulmonary toxicity. 11. Severe infection (NCI CTCAE ≥ Grade 3), such as severe pneumonia requiring hospitalization, bacteremia, or infectious complications, within 4 weeks prior to randomization, or active infection requiring systemic anti-infective therapy within 2 weeks prior to randomization. Participants receiving prophylactic anti-infective therapy (e.g., prophylaxis for urinary tract infection or chronic obstructive pulmonary disease exacerbation) may be eligible for enrollment after discussion with the Sponsor. 12. A superscan as seen in the baseline bone scan. 13. Active bleeding, a history of bleeding disorders, or treatment with coumarin anticoagulants. 14. Uncontrolled third-space fluid accumulation (e.g., pleural effusion, ascites, or pericardial effusion) requiring repeated drainage. 15. Participants of childbearing potential who are unwilling to use an acceptable method of contraception during the study and for 6 months after the last study drug administration. 16. Diagnosed with other malignancies that are expected to alter life expectancy or may interfere with disease assessment. However, patients with a prior history of malignancy that has been adequately treated and who have been disease free for more than 3 years are eligible, as are patients with adequately treated non-melanoma skin cancer, superficial bladder cancer. 17. Active chronic hepatitis B infection \[e.g., positive hepatitis B surface antigen (HBsAg) and/or hepatitis B core antibody (HBcAb) with HBV DNA ≥2,000 IU/mL or ≥5,000 copies/mL\], active hepatitis C infection \[e.g., positive hepatitis C virus (HCV) antibody with detectable HCV RNA\], HIV antibody positivity, or active syphilis infection (positive syphilis-specific antibody and non-treponemal antibody). 18. Known hypersensitivity to the components of the study therapy or its analogs. 19. Transfusion for the sole purpose of making a subject eligible for study inclusion. 20. Any disease, psychiatric condition, or surgical condition that may affect completion of the study (including poor compliance) or render the participant unsuitable for treatment with the investigational medicinal product. 21. Any other condition that, in the opinion of the investigator, makes the participant unsuitable for participation in this clinical study.