Neoadjuvant Lu-PSMA Radioligand Therapy and Ipilimumab in Men With Very High-risk Prostate Cancer

Inclusion Criteria: 1. Must be ≥18 years of age 2. Signed an informed consent form (ICF) indicating that the participant understands the purpose of and procedures required for the study and is willing to participate in the study; participants must be willing and able to adhere to the prohibitions and restrictions specified in this protocol 3. Histologically confirmed adenocarcinoma of the prostate including following criteria: Very High-risk defined by a total Gleason-Score ≥4+4 (ISUP-GG 4+5) and clinical stage cT3 (digital rectal examination or imaging based) plus clinical nodal status cN+ or Serum-PSA level \>20ng/ml 4. Exclusion of metastases (M0) on conventional imaging and maximum oligometastatic status on PSMA PET imaging 5. Treatment naïve patients 6. Eastern Cooperative Oncology Group ECOG 0-1 7. Candidate for radical prostatectomy with pelvic lymph node dissection as per the investigator 8. Patients must be PSMA Positron Emission Tomography (PET) scan positive with a prostatic SUVmax \> 12 (PRIMARY Score: 5) . 9. Following laboratory criteria must be obtained within 14 days prior to randomization: * Bone marrow reserve * White blood cells, WBC ≥ 2000/μL * Neutrophils ≥ 1500/μL * Platelets ≥ 100 x103/μL * Hemoglobin ≥ 9.0 g/dL * Hepatic: * AST/ALT ≤ 3 x ULN * Total Bilirubin ≤ 1.5 x ULN (except participants with Gilbert Syndrome, who may have total bilirubin \< 3.0 mg/dL) * Renal: * Serum creatinine ≤ 1.5xULN * Endocrine: * TSH 0,4 - 4,0 mU/l = 0,4 - 4,0 μU/ml * If TSH is not in normal range, fT3 and fT4must be determined fT3 2,3 - 4,5 pg/ml = 3,5 -7,0 pmol/l fT4 0,8 - 1,8 ng/dl = 8 - 18 ng/l = 10 - 23 pmol/l * Albumin \>3.0 g/dL (3.0 g/dL is equivalent to 30 g/L) * Electrolytes: * Potassium: 3.5-5 mmol/L * Sodium: 135-145 mmol/L * Pancreatic: * amylase, lipase ≤ 3 x ULN * alkaline phosphatase (range to be assessed in context of oligometastatic disease) * blood sugar \< 200 mg/dL (11.1 mmol/L) 10. Sexually active patients must use a condom to prevent them from fathering a child and to prevent delivery of study treatment via seminal fluid to their partner for at least 14 weeks after the last dose of \[177Lu\]Lu-PSMA-617. 11. Tumor tissue of both prostate biopsy and radical prostatectomy specimen available for local histology review and reference pathology by Professor Henning Reis (Department of Pathology, University Hospital Frankfurt). Exclusion Criteria: 1. Distant metastasis (clinical stage M1) on conventional imaging. Oligometastatic patients on exclusively PSMA PET imaging will not be excluded. Patients with PSA values below 20ng/ml and no evidence of nodal disease are excluded. 2. Prior treatment with androgen receptor antagonists. Treatment with GnRH analogs prior to ICF signature 3. Bilateral orchiectomy 4. History of prior systemic or local therapy for prostate cancer, including pelvic radiation for prostate cancer 5. Use of any investigational agent ≤4 weeks prior to randomization or any therapeutic procedure for prostate cancer at any time 6. Major surgery ≤4 weeks prior to randomization 7. Prior therapy with CTLA4 antibodies 8. Previous treatment with any of the following within 6 months of randomization: * Strontium-89, Samarium-153, Rhenium-186, Rhenium- 188, Radium-223, * Previous PSMA-targeted radioligand therapy 9. Any immunosuppressive therapy given within the past 30 days prior to study drug administration (excluding physiologic steroid hormone replacement and / or steroid therapy up to a maximum dose of 10 mg prednisone or equivalent per day) 10. Other concurrent cytotoxic chemotherapy, immunotherapy, radioligand therapy, or investigational therapy 11. Lack of availability for clinical follow-up assessments. 12. Other potential life-threatening malignancies within the past five years requiring treatment 13. Serious cardiac, gastrointestinal, hepatic or pulmonary disease reducing life expectancy to less than five years 14. Patients with serious intercurrent illness, requiring hospitalization. 15. Other serious illnesses, e.g., serious infections requiring antibiotics or bleeding disorders. 16. Patients carrying organ transplants and/or receiving continuous immunosuppressive medication (other than steroid therapy of up to 10 mg prednisone per day) 17. The patient is known to be positive for Human Immunodeficiency Virus (HIV) or other chronic infections (HBV, HCV) or has another confirmed or suspected immunosuppressive or immunodeficient condition. 18. Known hypersensitivity reaction to any of the components of study treatment 19. Known alcohol or drug abuse 20. Participation in another clinical study and use of any investigational or non-registered product (drug or vaccine) other than the study treatment within the 30 days before registration 21. Significant disease or condition which, in the investigator's opinion, would exclude the patient from the study 22. Legal incapacity or limited legal capacity