This study is a prospective, single-center, single-arm clinical trial consisting of two parts. In Part A, 3 participants were enrolled to receive sequential administrations of low doses of [177Lu]Lu-PSMA-137 and [177Lu]Lu-PSMA-617. Pharmacokinetics（PK） sampling and single-photon emission computed tomography/computed tomography (SPECT/CT) scans were performed at scheduled time according to the protocol. Based on quantitative pharmacological results, the optimal dosing regimen for [177Lu]Lu-PSMA-137 was derived. In Part B, 3 participants were enrolled to receive treatments with 50% and 100% of the optimal dose of [177Lu]Lu-PSMA-137, to preliminarily evaluate the safety, tolerability, radiation dosimetry, and efficacy of [177Lu]Lu-PSMA-137 in participants with metastatic castration resistant prostate cancer (mCRPC).

Inclusion Criteria:

• Before initiating any assessment process, written informed consent must be obtained from the subject.
• The participant must be an adult male aged 18 years or older, with an expected lifespan of more than 6 months.
• The participant must have a confirmed diagnosis of prostate cancer based on histological, pathological, and/or cytological examination.
• The participant 's [18F]F-PSMA-137 positron emission tomography/computed tomography (PET/CT) scan results must be positive, specifically defined as the presence of prostate specific membrane antigen (PSMA) positive lesions or metastatic lesions with tumor PSMA expression higher than liver parenchyma; no PSMA-negative metastatic lesions: presence of lymph node metastatic lesions with a short diameter of no less than 2.5cm and PSMA concentration lower than liver parenchyma; presence of soft tissue metastatic lesions with a short diameter of no less than 1cm and PSMA concentration lower than liver parenchyma; presence of metastatic bone lesions invading soft tissue, with the soft tissue having a short diameter of no less than 1cm and PSMA concentration lower than liver parenchyma.
• The participant's serum/plasma testosterone level must be maintained below the castrate level (i.e., <50 ng/dL or <1.7 nmol/L).
• The participant must have received at least one androgen receptor pathway inhibitors(ARPI) (such as enzalutamide and/or abiraterone) treatment and experienced treatment failure.
• The participant must have received at least one but no more than two taxane-based drug treatment regimens and experienced treatment failure; a taxane-based drug treatment regimen is defined as exposure to at least two cycles of taxane drugs. If the participant has only received one taxane-based drug treatment regimen and their doctor assesses that they are unsuitable for a second taxane-based drug treatment regimen due to reasons such as frailty or intolerance, the subject may still be included in the study.
• The records confirm the progressive mCRPC based on at least one of the following criteria:Serum/plasma prostate specific antigen (PSA) progression is defined as an increase in PSA levels measured in two separate instances at least one week apart, with a minimum starting value of 2.0 ng/mL.Soft tissue progression according to the modified response evaluation criteria in solid tumors version version 1.1 by prostate cancer working group 3 (PCWG3) (Eisenhauer et al., 2009; Scher et al., 2016).Bone disease progression: the presence of two new bone lesions; bone scan positivity alone defines metastatic disease to bone [PCWG3 criteria (Scher et al., 2016)].
• Prior to enrollment, participant must have had baseline computed tomography (CT), magnetic resonance imaging (MRI), or bone scan imaging obtained within ≤ 21 days, indicating the presence of ≥ 1 metastatic lesion, with at least one measurable lesion as determined by the modified RECIST version 1.1 by PCWG3.
• Participant must have adequate organ function, including:Bone marrow reserve: white blood cell (WBC) count ≥ 2.5×109/L or absolute neutrophil count (ANC) ≥ 1.5×109/L, platelet count ≥ 100×109/L, and hemoglobin ≥ 9 g/dL.Liver: total bilirubin ≤ 1.5× the upper limit of normal (ULN). For subjects with known Gilbert's syndrome, ≤ 3× ULN is acceptable; alanine aminotransferase (ALT) or aspartate aminotransferase (AST) ≤ 3.0× ULN or ≤ 5.0× ULN for subjects with liver metastases.

Kidney: estimated glomerular filtration rate (eGFR) ≥ 50 mL/min/1.73 m2, calculated using the Modification of Diet in Renal Disease (MDRD) formula.Albumin level: > 3.0 g/dL.

• ECOG (Eastern Cooperative Oncology Group) performance status score must be 0 - 2.

Exclusion Criteria:

• Within 6 months prior to enrollment, participant who have received radionuclide therapy such as strontium-89, samarium-153, rhenium-186, rhenium-188, radium-223, or hemibody radiotherapy;
• Participant who have previously received PSMA-targeted radioligand therapy;
• Participant who require radiotherapy, chemotherapy, immunotherapy, or other anti-tumor treatments within 28 days prior to enrollment or during the trial;
• Participant who have participated in any other clinical trial within 28 days prior to enrollment;
• Participant with a history of hypersensitivity to any study drug, its excipients, or drugs of similar chemical classes;
• Participant with a history of central nervous system (CNS) metastases, neurological instability, symptoms, or requiring glucocorticoids to maintain neurological stability; however, participant with CNS metastases who have received treatment (surgery, radiotherapy, gamma knife, etc.), are asymptomatic with stable neurological function, and are not using corticosteroids are eligible to participate in the study; participant with epidural disease, spinal canal disease, and previously treated areas of spinal cord involvement that are stable and without neurological impairment are also allowed;
• Participant with super-bone imaging observed on baseline bone scans;
• Symptomatic spinal cord compression or clinical or radiological findings suggestive of impending spinal cord compression; A history or current diagnosis of the following electrocardiogram (ECG) abnormalities, indicating significant safety risks for the participant: clinically significant arrhythmias such as sustained ventricular tachycardia, complete left bundle branch block, high-degree atrioventricular block (e.g., bifascicular block, Mobitz type II, and third-degree atrioventricular block); cardiac or cardiac repolarization abnormalities, including any of the following: a history of myocardial infarction (MI), angina, or coronary artery - bypass grafting (CABG) within 6 months prior to signing the informed consent form (ICF);
• Accompanied by severe (as determined by the principal investigator) medical conditions, including but not limited to new york heart association class III or IV congestive heart failure, a history of congenital long QT syndrome, uncontrolled infection, known active hepatitis B or C, or other significant illnesses that the investigator believes may affect study participation or compliance; subjects with human immunodeficiency virus (HIV) infection at low risk for acquiredImmune deficiency syndrome，(AIDS) related outcomes may participate in this trial;
• A diagnosis of other malignancies that may alter life expectancy or potentially interfere with disease assessment. Participant with a prior history of malignancy before enrollment, but who have received adequate treatment and have been disease-free and treatment-free for more than 3 years, are eligible to participate in the study, as are participant with adequately treated non-melanoma skin cancer and superficial bladder cancer.
• Sexually active men were unwilling to use condoms during sexual intercourse during the study treatment period and within 14 weeks after stopping the study treatment. All sexually active male participant must use condoms to prevent their partners from getting pregnant and prevent the transmission of study treatment drugs to their partners through semen. In addition, male participant must not donate sperm within the above-mentioned time frame;
• With uncontrollable bladder outflow obstruction or urinary incontinence. Note: Participant with bladder outflow obstruction or urinary incontinence are eligible to participate in the study if they can be controlled through the best available standard treatments (including urine pads and drainage);
• History of physical or mental illness/condition that may interfere with the purpose and evaluation of the study;
• Any condition that prevents the participant from assuming an arm-raising position.