The Safety and Dosimetry Study of 177Lu-LNC1003 Injection

Inclusion Criteria: * Patients or authorized guardians must have the ability to understand and sign an approved informed consent form (ICF). * Patients must have the ability to understand and comply with all protocol requirements. * Patients must be aged 21 years or older. * Patients must have histological, pathological, and/or cytological confirmation of PC that is refractory to or has progressed following prior treatments. * Patients must have ≥ 1 metastatic lesion present on baseline and documented progressive mCRPC based on the Prostate Cancer Working Group 3 (PCWG3) criteria; patients must fill at least one of the following criteria: * PSA progression * Objective radiographic progression in soft tissue * New bone lesions * Patients must have a castrate level of serum/plasma testosterone (\&lt; 50 ng/dL or \&lt; 1.7 nmol/L). * Patients must have received treatment with at least one prior novel androgen receptor pathway inhibitor (such as enzalutamide, apalutamide, and/or abiraterone). * Patients must have been deemed not suitable for chemotherapy, i.e., the patient refused chemotherapy or was judged unsuitable for chemotherapy by the doctor. Alternatively, patients may have been previously treated with at least one, but no more than two previous taxane regimens, or have been offered, but declined, or been ineligible for taxane-based chemotherapy. A taxane regimen is defined as a minimum exposure of 2 cycles of a taxane. If a patient has received only one taxane regimen, the patient is eligible if: a. The patient\&#39;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 at least 1 measurable lesion as defined by Response Criteria in Solid Tumors (RECIST) version 1.1. * Patients must be 68Ga-PSMA-11 PET/CT scan positive. * Patients must have an Eastern Cooperative Oncology Group performance status (ECOG PS) score of 0 or 1. * Patients must have an adequate organ function, in the absence of clinical intervention within 28 days before the administration of the 177Lu-LNC1003, as defined by: Hemoglobin (Hb) \> 9.0g/dL White blood cell (WBC) count ≥ 3 x 109/L or absolute neutrophil count (ANC) \>1.5 x 109/L Platelets ≥ 100 x 109/L International normalized ratio (INR) \<1.5 for patients that are not on warfarin Prothrombin time (PTT) \< 2 x ULN Total bilirubin \<1.5 x ULN Serum albumin \>3.0 g/dL Alanine aminotransferase (ALT) \<3 x ULN, or\<5 x ULN if deemed related to liver metastases from solid tumor Aspartate aminotransferase (AST) \<3 x ULN, or\<5 x ULN if deemed related to liver metastases from solid tumor Creatinine clearance ≥ 60 mL/min (calculated using the Cockcroft-Gault formula). * All other toxicity parameters, except for alopecia, must be NCI-CTCAE v.5.0 Grade 0 or 1. * Sexually active participants with female partners of childbearing potential are eligible to participate if they agree to follow 1 of the following methods of contraception consistently, starting from screening, during the study and for at least 14 weeks after the last dose of 177Lu-LNC1003 Injection: Are abstinent from penile-vaginal intercourse as their usual and preferred lifestyle (abstinent on a long-term and persistent basis) and agree to remain abstinent; Are sterilized (with the appropriate post-vasectomy documentation of the absence of sperm in the ejaculate); Agree to use a male condom and have their partner use a contraceptive method with a failure rate of \&lt; 1% per year as described below when having penile-vaginal intercourse with a woman of childbearing potential who is not currently pregnant, and who agrees to the use of a condom by her partner. * Participants must agree to refrain from donating sperm starting from Screening, during the study and for at least 14 weeks after the last dose of 177Lu-LNC1003 Injection. * Sexually active participants with a pregnant or breastfeeding partner must agree to remain abstinent from penile vaginal intercourse; or use a male condom during each episode of penile penetration during the study. Exclusion Criteria: * Other identified malignancies within 5 years in addition to radically treated locally curable malignant tumors, such as basal or squamous cell skin cancer, superficial bladder cancer. * Previous treatment with any of the following within 6 months before enrollment: Strontium-89, Samarium-153, Rhenium-186, Rhenium-188, Radium-223, hemi-body irradiation, 177Lu-PSMA-617 (Pluvicto) and any investigational beta-emitting radiotherapeutics. * Any systemic anti-cancer therapy (e.g. PSMA-targeted radioligand therapy, chemotherapy, immunotherapy or biological therapy \[including monoclonal antibodies\]) within 28 days prior to day of enrollment * Any investigational agents within 28 days of enrollment * Other concurrent cytotoxic chemotherapy, immunotherapy, radioligand therapy, or investigational therapy * Transfusion for the sole purpose of making a subject eligible for study inclusion * History of allergic reactions attributed to compounds of similar chemical or biologic composition to 177Lu-LNC1003 as assessed from medical records * Participants who have not fully recovered from major surgery or significant traumatic injury prior to the first dose of study drug or expects to have major surgery during the study period or within 3 months after the last dose of study drug * Life expectancy \&lt; 6 months as assessed by the treating physician * Other serious illness(es) involving the cardiac, respiratory, CNS, renal, hepatic or hematological organ systems which might preclude completion of this study or interfere with determination of causality of any adverse effects experienced in this study * A superscan; i.e., very high ratio of bone to background uptake due to high osteoblastic activity, as seen in the baseline Tc-99m diphosphonate bone scan. * Clinically significant abnormalities on electrocardiogram (ECG) at screening including QTcF \&gt; 470 ms, and subjects who cannot tolerate high volume load. * Active and clinically significant bacterial, fungal, or viral infections, including hepatitis B (HBV), hepatitis C (HCV), know human immunodeficiency virus (HIV), or acquired immunodeficiency syndrome (AIDS)-related illness (patients with treated HIV and hepatitis B or C could be included) * Known brain metastases and/or carcinomatous meningitis, unless these metastases have been treated and stabilized * Uncontrolled diabetes mellitus as defined by a HbA1c \&gt; 9% * Prior external beam radiation therapy involving \&gt; 25% of the bone marrow * Unmanageable urinary incontinence including physical outflow obstructions rendering the administration of 177Lu-LNC1003 unsafe. * Unable to comply with relevant contact precautions post 177Lu-LNC1003 treatment. * Any other condition, assessed by the investigator, that may increase the risk associated with study participation, interfere with the study interpretation, or in any other way make the subject unsuitable for participation in the study.