Lutetium (177Lu) DGUL Combined With Pembrolizumab in Metastatic Castration-Resistant Prostate Cancer

Inclusion Criteria: * Male patients aged 19 years or older. * Patients with histopathologically or cytologically confirmed adenocarcinoma of the prostate, without neuroendocrine or small cell differentiation, who have metastatic disease documented by bone lesions/soft tissue lesions and are not eligible for curative treatment. * Patients with serum testosterone levels meeting castration levels (\< 50 ng/dL) at the screening visit. * Patients must have experienced disease progression following treatment for mCRPC with a second-generation androgen receptor signaling inhibitor therapy (e.g., abiraterone or enzalutamide). * Docetaxel treatment is allowed for localised prostate cancer and at mHSPC stage if more than 12 months have elapsed from the last dose of docetaxel, as long as no signs of failure or disease progression occurred during or immediately after such treatment. * Patients must be receiving hormone deprivation therapy limited to the use of LHRH agonists or LHRH antagonists throughout the study. For patients who have not undergone bilateral orchiectomy, medical castration with an LHRH agonist or antagonist must have been initiated at least 4 weeks prior to baseline and must be maintained for the entire study duration. * Patients with prostate specific membrane antigen (PSMA)-positive disease, with a maximum standardized uptake value (SUVmax) of at least 20 at a site of disease and greater than 10 at other disease sites measuring ≥ 10mm in longest diameter. * Patients with an Eastern Cooperative Oncology Group (ECOG) performance status of ≤ 1. * Patients with a life expectancy of at least 6 months. * Patients with adequate hematologic, renal, and liver function, confirmed by the following criteria: * Absolute neutrophil count (ANC) ≥ 1,500/μL (without granulocyte colony stimulating factor (G-CSF) administration within 2 weeks prior to baseline) * Platelet count ≥ 100,000/μL (without transfusion within 2 weeks prior to baseline) * Hemoglobin ≥ 9.0 g/dL (without transfusion within 4 weeks prior to baseline) * Serum creatinine ≤ 1.8 mg/dL or Cockcroft-Gault creatinine clearance (CrCl) formula \> 40 ml/min * Aspartate transaminase (AST) and alanine transaminase (ALT) ≤ 2.5 times the upper limit of normal (ULN), or ≤ 5 times the ULN for patients with confirmed liver metastasis * Total bilirubin ≤ 1.5 times ULN (except in patients with Gilbert syndrome) * Prothrombin time (PT) and activated partial thromboplastin time (aPTT) ≤ 1.5 times ULN * Patients who have AEs due to previous anticancer therapies must have recovered to ≤ Grade 1 or baseline. Patients with endocrine-related AEs who are adequately treated with hormone replacement or patients who have ≤ Grade 2 neuropathy are eligible. * Patients who voluntarily agree to participate in the clinical trial and sign the informed consent form. Exclusion Criteria: * Known additional malignancy that is progressing or has required active treatment within the past 3 years (Patients with basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or carcinoma in situ, excluding carcinoma in situ of the bladder, that have undergone potentially curative therapy are not excluded). * Patients who have received chemotherapy, biological therapy, or immunotherapy for prostate cancer within 4 weeks from baseline (6 weeks in the case of nitrosoureas or mitomycin). * Any prior treatment with taxane chemotherapy for mCRPC. * Patients with history of allogeneic stem cell transplantation (alloSCT), or solid organ transplantation. * Patients who have received high-dose chemotherapy requiring hematopoietic stem cell treatment, within 2 years from baseline. * Patients who have previously received PSMA-targeted treatment (e.g., radiotherapy, immunotherapy, or antibody-drug conjugate) or those treated with radiopharmaceuticals such as radium-223 within 6 months from baseline. * Patients who have previously received radiotherapy (RT) to the lung \> 30 Gy within 6 months of the first dose. * Prior exposure to any anti-programmed cell death protein 1(PD-1), anti-programmed death ligand 1/2 (PD-L1/L2), or anti- cytotoxic T lymphocyte antigen-4 (CTLA-4) antibody, or any other agent specifically targeting T cell co-stimulation or immune checkpoint pathways. * Diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior the first dose of study intervention. * Known active central nervous system (CNS) metastases and/or carcinomatous meningitis. Patients with previously treated brain metastases may enroll if they are radiologically stable (i.e., without evidence of progression) for at least 4 weeks, as confirmed by repeat imaging during the study screening. They must also be clinically stable and must not have required steroid treatment for at least 4 weeks before receiving the first dose of the study intervention. * Patients with the following medical history or history of surgery/procedures: * Deep vein thrombosis (DVT) or pulmonary embolism (PE) within 1 year from baseline. * Cytomegalovirus (CMV) or Epstein-Barr virus (EBV) infection within 6 months from baseline. * Acute coronary syndrome (unstable angina or myocardial infarction) within 6 months from baseline. * Major cerebrovascular disease, such as stroke, within 6 months from baseline. * General anesthesia or major surgery requiring respiratory assistance within 4 weeks from baseline (video-assisted thoracoscopic surgery or open-and-closed (ONC) surgery allowed within 2 weeks). * Active autoimmune disease that has required systemic treatment in past 2 years except replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid). * History of (noninfectious) pneumonitis/interstitial lung disease that required steroids or has current pneumonitis/interstitial lung disease. * Patients with the following conditions: Cl