Inclusion Criteria:  Patients must be ≥ 18 years of age.  Patients must have progressive mCRPC. Documented progressive mCRPC will be based on at least 1 of the following criteria:  Rising PSA according to PCWG3 criteria (2 rising values above a baseline at a minimum of 1-week intervals) and PSA ≥2.0 ng/mL Soft-tissue progression defined as per prostate cancer working group 3 (PCWG3)-modified RECIST v1.1 Progression of bone disease as per PCWG3 criteria Patients must have mCRPC with histological, pathological, and/or cytological confirmation of adenocarcinoma of the prostate. Patients must have ≥ 1 metastatic lesion that is present on baseline CT, MRI, or bone scan imaging. Patients must have prostate-specific membrane antigen (PSMA)- positive prostate cancer, as determined by PSMA-targeted PET / CT scan. Patients must have a castrate level of serum/plasma testosterone (< 50 ng/dL or < 1.7 nmol/L). Patients must have received at least one NAAD (such as enzalutamide and/or abiraterone).  Patients must have been previously treated with at least 1, but no more than 2 previous taxane regimens. A taxane regimen is defined as a minimum exposure of 2 cycles of a taxane. If a patient has received only 1 taxane regimen, the patient is eligible if:  a. The patient's physician deems him unsuitable to receive a second taxane regimen (e.g. frailty assessed by geriatric or health status evaluation, intolerance, etc.).  Patients must have recovered to ≤ Grade 2 from all clinically significant toxicities related to prior therapies (i.e. prior chemotherapy, radiation, immunotherapy, etc.).  Patients must have adequate organ function:  Bone marrow reserve:  White blood cell (WBC) count ≥ 2.5 x 10^9/L (2.5 × 10^9/L is equivalent to 2.5 × 10^3/μL and 2.5 × K/μL and 2.5 × 10^3/cumm and 2500/μL) OR absolute neutrophil count (ANC) ≥ 1.5 × 10^9/L (1.5 × 10^9/L is equivalent to 1.5 × 10^3/μL and 1.5 × K/μL and 1.5 × 10^3/cumm and 1500/μL). Platelets ≥ 100 × 10^9/L (100 × 10^9/L is equivalent to 100 × 10^3/μL and 100 × K/μL and 100 × 10^3/cumm and 100 000/μL). Hemoglobin ≥ 9 g/dL (9 g/dL is equivalent to 90 g/L and 5.59 mmol/L).  Hepatic:  Total bilirubin ≤ 1.5 × the institutional upper limit of normal (ULN). For patients with known Gilbert's Syndrome ≤ 3 × ULN is permitted. Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 3.0 × ULN OR ≤ 5.0 × ULN for patients with liver metastases.  Renal:  Serum/plasma creatinine ≤ 1.5 × ULN or creatinine clearance ≥ 50 mL/min. Albumin > 3.0 g/dL (3.0 g/dL is equivalent to 30 g/L).  Exclusion Criteria:  History of hypersensitivity to any drugs or metabolites of similar chemical classes as Lu-PSMA-617. Other concurrent cytotoxic chemotherapy, immunotherapy, radioligand therapy, or investigational therapy. Transfusion for the sole purpose of making a subject eligible for study inclusion. 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. For patients with parenchymal CNS metastasis (or a history of CNS metastasis), baseline and subsequent radiological imaging must include evaluation of the brain (MRI preferred or CT with contrast). Any pre-existing symptoms, or concurrent severe and/or uncontrolled medical conditions which could compromise safe participation in the MAP. Not able to understand and comply with treatment instructions and requirements.