177Lu-PSMA-617 With Liver Directed Therapy in Metastatic Castration Resistant Prostate Cancer

Inclusion Criteria: 1. Histologically confirmed prostate cancer. 2. Progressive disease by PCWG3 criteria at study entry. 3. Male participants who are at least 18 years of age on the day of signing informed consent. 4. Castrate level of serum testosterone at study entry (\< 50 ng/dL). Note: Participants without prior bilateral orchiectomy are required to remain on Luteinizing hormone-releasing hormone (LHRH) analogue treatment for duration of study treatment. 5. Prior progression on at least one second generation androgen signaling inhibitor including abiraterone, apalutamide, darolutamide, and/or enzalutamide. 6. Adverse events related to prior anti-cancer treatment (excluding LHRH analogs) must have recovered to Grade ≤ 1 (except for any grade alopecia and grade ≤ 2 neuropathy). 7. Prior external beam radiotherapy is allowed if the last radiotherapy treatment was greater than 2 weeks from start of study treatment on Cycle 1 Day 1 (C1D1). Note: Participants must have recovered from all radiation-related toxicities. A 1-week washout is permitted for palliative radiation (≤2 weeks of radiotherapy) to non-central nervous system (CNS) disease. 8. At least one PSMA-avid extrahepatic lesion on screening PSMA Positron Emission Tomography (PET). A positive lesion is defined as uptake above background liver. Hepatic lesions may be PSMA PETnegative or positive. 9. Availability of archival mCRPC tissue, or presence of a metastatic lesion that is amenable to fresh biopsy and willingness to undergo biopsy during screening if no archival mCRPC tissue available. 10. The presence of one or more liver metastases amenable to liver-directed therapy in the judgment of the treating interventional radiologist. Liver metastases may be detected by CT or magnetic resonance imaging (MRI), and biopsy confirmation is not required. 11. Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 or Karnofsky ≥ 50%. 12. Demonstrates adequate organ function as defined below: 1. Absolute neutrophil count ≥ 1,500/ microliter (mcL). 2. Platelets ≥ 100,000/mcL. 3. Hemoglobin \> 9.0 g/dL. 4. Total bilirubin ≤ 1.5 x upper limit of normal (ULN). In participants with known or suspected Gilbert's disease, direct bilirubin ≤ ULN. 5. aspartate aminotransferase (AST)/serum glutamic-oxaloacetic transaminase (SGOT) ≤ 5 x institutional upper limit of normal. 6. alanine aminotransferase (ALT)/serum glutamic-pyruvic transaminase (SGPT) ≤ 5 x institutional upper limit of normal. 7. Prothrombin time ≤ 1.5 x institutional upper limit of normal (unless on medical therapy known to prolong prothrombin time). 8. Albumin ≥ 2.8 g/dL 9. Creatinine clearance Glomerular filtration rate (GFR) ≥ 30 mL/min/1.73 m2, calculated using the Cockcroft-Gault equation or 24 hour urine collection. 13. Participants with previously treated brain metastases are eligible provided the following criteria are all met: 1. Last treatment was \> 28 days prior to C1D1 2. No evidence of new/progressive brain metastases is observed on MRI obtained during the Screening window 14. Participants must use appropriate methods of contraception during study treatment and for at least 6 months after last study treatment. Note: Participants who are sexually active should consider their female partner to be of childbearing potential if she has experienced menarche and is not postmenopausal (defined as amenorrhea \> 24 consecutive months) or has not undergone successful surgical sterilization. Even women who use contraceptive hormones (oral, implanted, or injected), an intrauterine device, or barrier methods (diaphragms, condoms, spermicide) should be considered to be of childbearing potential. Participants who have undergone vasectomy themselves should also be considered to be of childbearing potential. Acceptable methods of contraception include continuous total abstinence, or double barrier method of birth control (e.g., condoms used with spermicide, or condoms used with oral contraceptives). Periodic abstinence and withdrawal are not acceptable methods of contraception. 15. Ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: 1. De novo small cell neuroendocrine prostate cancer. 2. One or more extrahepatic soft tissue lesions (lymph nodes \> 1.5 cm in short axis, visceral/soft tissue lesions \> 1 cm) on screening CT that is negative on PSMA PET. Non- PSMA avid liver lesions are allowed. 3. Recipient of other systemic anti-cancer therapies administered within 14 days, or 5 half lives, whichever is shorter, prior to initiation of study treatment. Note: LHRH analogues are the exception and are permitted 4. Recipient of prior PSMA-directed radioligand treatment. 5. Recipient of \> 2 lines of prior taxane-based chemotherapy administered in the castration-resistant setting. Prior taxane in the castration sensitive setting does not count towards this limit. If platinum chemotherapy is added to taxane this does not count as a separate line of treatment. 6. Previous bilio-enteric anastomosis, ampulla of Vater sphincterotomy, biliary stent, or biliary drain passing through the ampulla of Vater. 7. Currently participating in a study of an investigational therapeutic agent or has used an investigational device within 4 weeks prior to the first dose of study treatment on C1D1. Note: Participants who have entered the follow-up phase of an investigational study may participate as long as it has been 4 weeks after the last dose of the previous investigational agent. 8. Clinically significant cardiovascular disease including, but not limited to: 1. Uncontrolled or any New York Heart Association Class 3 or 4 congestive heart failure. 2. Uncontrolled angina, history of myocardial infarction, unstable angina, or stroke within 6 months before study entry. 3. Clinically significant arrhythmias not controlled by medication. Note: Chronic rate-controlled or paroxysmal atrial fibrillatio