177Lu-DOTA-TLX591 Safety, Biodistribution and Dosimetry Study

Inclusion Criteria: * Be male, at least 18 years old, with histologically/pathologically confirmed metastatic adenocarcinoma. * Be of ECOG Performance Status 0, 1, or 2 and have an estimated life expectancy of ≥ 6 months. * Have metastatic disease (≥1 metastatic lesions present on baseline whole body CT, MRI, or bone scintigraphy). * Have castration-resistant PC (defined as disease progressing despite castration by orchiectomy or ongoing use of luteinizing hormone-releasing hormone \[LHRH\] agonists) and must have a castrate level of serum/plasma testosterone (\< 50 ng/dL or \<1.7 nmol/L). * In the mCRPC setting, must have received a minimum of 12 weeks of prior therapy with a NAAD, either enzalutamide or abiraterone plus prednisone. * Have received one line of prior taxane therapy, or have refused or are ineligible for taxanes * Have disease that is progressing at study entry, despite a castrate testosterone level (\<50 ng/dL or \<1.7 nmol/L), by the demonstration of at least one of the following: 1. Increase in PSA greater than 25% and \> 2 ng/mL above nadir, confirmed by progression at 2 timepoints at least 3 weeks apart. 2. Progressive disease or new lesion(s) (relative to previous imaging) in the viscera or lymph nodes as per RECIST1.1 or in bone as per Prostate Cancer Working Group 3 \[PCWG3). Any ambiguous results are to be confirmed by additional imaging modality (e.g., CT, Tc-99m bone scintigraphy) * Have disease which is PSMA positive, as demonstrated by a 68Ga-PSMA-11 PET/CT or \[18F\]DCFPyL PET/CT scan and confirmed as eligible by local reader (patient must have at least one site of metastatic disease with SUVmax ≥1.5 times the SUV of normal liver). If the disease meets the criteria for PSMA positivity, but there is one or more soft tissue lesion of ≥2 cm that is not PSMA positive, then the patient is to be excluded on the grounds that there is substantial disease which might not respond to the therapy. * Must have recovered to ≤ Grade 2 from all clinically significant toxicities related to prior therapies (i.e., surgery, local radiotherapy, NAAD, chemotherapy, etc.). * Can be receiving a bisphosphonate or denosumab regimen provided tolerance to this therapy has been proven. 11\. Have adequate organ function at Screening: a. Bone marrow: i. Platelets ≥150×109/L ii. Absolute neutrophil count \>1.5×109/L iii. Hemoglobin ≥10g/dL (no red blood cell transfusion in the previous 4 weeks) b. Liver function: i. Total bilirubin ≤1.5×the upper limit of normal (ULN). For patients with known Gilbert's Syndrome ≤3×ULN is permitted ii. Alanine aminotransferase (ALT) or aspartate aminotransferase (AST) ≤3×ULN OR ≤5×ULN for patients with liver metastases c. Renal function: i. Serum/plasma creatinine ≤1.5×ULN or creatinine clearance ≥50 mL/min * Have the capacity to understand the study and be able and willing to comply with all protocol requirements. * Must comply with the radiation protection guidelines (including hospital admissions and isolation) that are applied by the treating institution in order to protect their contacts and the general public. * Must agree to practice adequate precautions to prevent pregnancy in a partner and to avoid potential problems associated with radiation exposure to the unborn child (Refer to Clinical Trials Facilitation Group, 2020: Recommendations related to contraception and pregnancy testing in clinical trials Version 1.1, CTFG, 2020). Exclusion: * Are unable, in the opinion of the Investigator, to understand or are unwilling to sign a written informed consent document or to follow investigational procedures. * Have PC with pathological findings consistent with small cell or any histology other than adenocarcinoma of the prostate. If there are minor elements of neuroendocrine histology, this is acceptable. * Experiencing uncontrolled pain * Diagnosed with other malignancies that are expected to alter life expectancy or may interfere with disease assessment. Patients with a prior history of malignancy that has been adequately treated and who have been disease-free for more than 3 years are eligible, as are patients with adequately treated non-melanoma skin cancer, and superficial bladder cancer. * At increased risk of hemorrhage, or with a recent history of a thrombotic event (e.g., deep vein thrombosis \[DVT\]/ pulmonary embolism \[PE\]) and/or are using long-term anti-coagulant or anti-platelet agents. * Have received prior administration of monoclonal antibody (mAb) J591 or HuJ591 or any other PSMA targeted therapy. * Have known allergies, hypersensitivity, or intolerance to the investigational drug or its excipients. * Have received systemic anti-cancer therapy (e.g., chemotherapy, immunotherapy, or biological therapy) and/or radiation therapy within 4 weeks of enrollment OR if any significant AEs have not resolved to National Cancer Institute (NCI) AE Criteria ≤2; OR are receiving other concurrent cytotoxic chemotherapy, immunotherapy, radioligand therapy, or investigational therapy. * Have received prior treatment with radiopharmaceuticals containing, but not limited to, the following radioisotopes: 89Strontium, 153Samarium, 186Rhenium, 188Rhenium, 223Radium; or have received hemi-body irradiation within 6 months prior to randomization. * Have received other investigational agents within 4 weeks of randomization. * Have known brain metastases (any size) or hepatic metastases \> 1 cm. * Have a history of seizure and/or stroke within past 6 months. * Have clinical or radiologic findings indicative of impending cord compression or experiencing symptomatic cord compression. * Have a serious active or sub-clinical infection, or angina pectoris or heart failure (New York Heart Association \[NYHA\] Class III or IV), significantly prolonged QT interval or other serious illness(es) involving the cardiac, respiratory, central nervous, renal, hepatic or hematological organ systems, which might impair the ability to complete this study or could interfere with determination of causality of any adverse effects experienced in this study, or which require treatment that could interact with study treatment. * Have received treatment with any PARP inhibitors (i.e., Olaparib) or with any platinum based anti-neoplastic drugs. * Have a known alteration in breast cancer genes (BRCA) BRCA1, BRCA2, or Ataxia Telangiectasia Mutated Gene (ATM) gene and are eligible to receive Olaparib therapy according to their treating institution SoC.