An Open-label, Multicentre, Integrated Phase 1 & 2 Study to Evaluate the Safety, Tolerability, Radiation Dosimetry and Anti-tumour Activity of Lutetium (177Lu) rhPSMA-10.1 Injection in Men With Metastatic Castrate-resistant Prostate Cancer

Inclusion Criteria: 1. Male subjects, 18 years of age or older with histologically confirmed adenocarcinoma of the prostate. 2. Serum testosterone levels \<50 ng/dL (1.73 nmol/L) after surgical or continued chemical castration. 3. Presence of disease target or non target lesions (per RECIST v1.1) on CT/MRI and/or presence of disease on full body 99mTc bone scan performed within 28 days of screening. 4. Positive disease expression of PSMA as confirmed on PSMA PET/CT scan. 5. At least 4 weeks or 5 half-lives (whichever is longer) elapsed between last anti-cancer treatment administration and the initiation of study treatment (except for Luteinising Hormone-releasing Hormone or GnRH). 6. Resolution of all previous treatment related toxicities to CTCAE version 5.0 grade of ≤1 (except for chemotherapy induced alopecia and grade 2 peripheral neuropathy or grade 2 urinary frequency which are allowed). 7. Prior major surgery must be at least 12 weeks prior to study entry. 8. Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 with a life expectancy ≥6 months. 9. Adequate bone marrow reserve and organ function as demonstrated by blood count, and serum biochemistry at baseline. 10. Adequate contraception for patients and their partners. 11. For Phase 1 mCRPC only: Subjects who have experienced disease progression on or after at least 1 NAAD (e.g. abiraterone, enzalutamide) and at least 1 course (but no more than 2 courses) of taxane-based chemotherapy. For Phase 2 mCRPC only: Subjects who have experienced disease progression on or after at least 1 NAAD (e.g. abiraterone, enzalutamide, apalutamide, darolutamide), but have not received previous taxane-based chemotherapy for the treatment of mCRPC. Exclusion Criteria: 1. Known hypersensitivity to the therapeutic or diagnostic IMP or any of its constituents. 2. Presence of significant PSMA-negative disease on ceCT/MRI scan 3. Diffuse marrow infiltration of disease ('superscan' appearance on full body 99mTc bone scan). 4. Symptomatic spinal cord compression, or clinical or radiological findings that are indicative of impending spinal cord compression. 5. Known history of haematological malignancy. 6. Known history of central nervous system (CNS) metastases. 7. Histological findings consistent with neuroendocrine phenotype of prostate cancer. 8. Known history of other solid malignancy that may reduce life expectancy and/or may interfere with disease assessment. 9. Unresolved urinary tract obstruction defined as radiographic evidence of hydronephrosis with or without ureteric stent/nephrostomy. 10. Any uncontrolled significant medical, psychiatric, or surgical condition or laboratory finding that would pose a risk to subject safety or interfere with study participation or interpretation of individual subject results. 11. Ongoing treatment with bisphosphonates for bone-targeted therapy. 12. Severe urinary incontinence that would preclude safe disposal of radioactive urine. 13. Single kidney or renal transplant or any concomitant nephrotoxic therapy that might put the subject at high risk of renal toxicity during the study in the judgement of the investigator. 14. Clinically significant abnormalities on a single 12 lead electrocardiogram (ECG) at screening. 15. Previously received external beam irradiation to a field that includes more than 30% of the bone marrow or kidneys. 16. Previous treatment with any of the following: PSMA targeted radionuclide therapy, Strontium-89, Samarium-153, Rhenium 186, Rhenium-188, Radium-223, hemi-body irradiation. 17. Subjects with bilateral hip replacements or any significant metallic implants or objects, that may affect image quality and/or dosimetry calculations. 18. Transfusion of blood products for the sole purpose of meeting the eligibility criteria for this clinical study. 19. Participation in other studies involving IMP(s) within 28 days or 5 half-lives (whichever is longer) prior to study entry and/or during study participation. 20. Any history of clinically significant parenchymal lung disease e.g. interstitial lung disease or bullous emphysema. 21. Any history of prior thoracic external beam radiotherapy. 22. Presence of abnormal PSMA PET uptake in the lung parenchyma above expected physiological levels, as determined by local assessment.