Standard of Care +/- 177Lu-PSMA-617 In de Novo mHSPC Patients With Poor PSA Response (PEACE6-Poor Responders)

Inclusion Criteria: All of the following criteria must be met ahead of randomization to satisfy trial eligibility requirements: 1. Signed a written informed consent form prior to any trial specific procedures. Note: In case of physical incapacitation, a trusted representative of their choice, which is not the Investigator or sponsor, can sign on the behalf of the patients. 2. Aged ≥18 years old 3. Life expectancy \> 6 months as per investigator estimate 4. Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 5. Men with histologically or cytologically confirmed adenocarcinoma of the prostate 6. De novo metastatic disease defined by clinical or radiographic evidence of metastases at diagnosis (i.e. before any treatment started). If not available, a more recent imaging can be used 7. Measurable disease or bone lesions evaluable according to PCWG3 criteria. Patients with doubtful bone metastases are not eligible 8. A pre-randomization 68Ga-PSMA-11 PET/CT scan performed within 4 weeks prior to randomization in the trial. FDG PET scan is not required for this protocol. All patients will be treated independently from the results of pre-randomization PSMA PET scan: patients with PSMA-positive or PSMA-negative disease according to PROMISE 2.0 criteria are eligible. 9. Have 6 to 8 months of previous AND ongoing standard systemic treatment for prostate cancer consisting in either: * ADT with an androgen receptor signaling inhibitor (ARSI) (i.e., abiraterone (plus prednisone), or apalutamide or enzalutamide) ± radiotherapy \*\* * ADT with docetaxel\* plus an ARSI (i.e. abiraterone (plus prednisone), or darolutamide,) ± radiotherapy\*\* Note: \*Docetaxel must have been stopped at least 4 weeks ahead of randomization. \*\* Previous radiotherapy to the primary tumor and/or to the metastases is accepted as long as it was not PSMA-based and must has been completed at least 4 weeks ahead of randomization. 10. Stable or declining PSA level but not a rising one 11. Serum PSA of ≥ 0.2 ng/mL at 6 to 8 months after systemic treatment initiation 12. Testosterone level \< 50 ng/dl or \< 1.7 nmol/L 13. Be fit enough for 177Lu-vipivotide tetraxetan treatment: * Adequate bone marrow function: hemoglobin ≥90 g/L (in absence of red blood cell transfusion within 4 weeks prior to randomization), absolute neutrophil count ≥1.5 x10⁹/L, platelet count \>100 x10⁹/L * Adequate liver function: aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤2.0 x upper limit of normal (ULN), or ≤ 5.0 x ULN in the presence of liver metastases; bilirubin \<1.5 x ULN (unless known or suspected Gilbert syndrome, then \<3 x ULN is permitted) * Adequate renal function: calculated creatinine clearance ≥ 50 ml/min (using the MDRD or CKD EPI method). 14. For sexually active men with female partners of reproductive potential or with pregnant women, agreement to use a condom with another effective contraceptive method during trial participation and up to 14 weeks after study treatment completion. 15. Affiliated to the social security system or in possession of equivalent private health insurance (according to local regulations for participation in clinical trials). 16. Willing and able to comply with the protocol for the duration of the trial including undergoing treatment and scheduled visits, and examinations including follow-up. Exclusion Criteria: Patients presenting with any of the following criteria are not eligible: 1. Any evidence of cancer progression (including a rising PSA level, clinical progression, or radiological progression) 2. Prior or concurrent PSMA-based radioligand therapy or other PSMA target treatments 3. Known hypersensitivity to the components of the study therapy or its analogs 4. Any condition preventing the use of the standard of care and/or specific experimental treatments tested in the trial 5. Any of the following within 6 months before randomization: stroke, myocardial infraction, severe/unstable angina pectoris, coronary/peripheral artery bypass graft, congestive heart failure New York Heart Association (NYHA) Class III or IV 6. Hypertension not controlled by an anti-hypertensive treatment (systolic blood pressure \[sBP\] ≥ 160 mmHg or diastolic blood pressure \[dBP\] ≥ 95 mmHg, 3 consecutive measures taken 5 minutes apart) 7. Severe or uncontrolled concurrent disease, infection or co-morbidity 8. Pathological findings consistent with small cell carcinoma of the prostate 9. History of malignancy within 3 years of the current diagnosis with the exception of successfully treated basal cell or squamous cell skin carcinoma 10. Ongoing participation in another clinical trial involving an investigational product.. Treatment with an investigational product must have ended within 28 days prior to the day of randomization 11. Patients unwilling or unable to comply with the medical follow-up required by the trial because of geographic, familial, social, or psychological reasons 12. Persons deprived of their liberty or under protective custody or guardianship