Inclusion Criteria:
1. Subject must have the ability to understand and sign an approved informed consent form (ICF).
2. Aged 18 years or older, regardless of sex.
3. Histologically or cytologically confirmed RAIR-DTC subject who has failed TKIs treatment or refuse standard therapy.
4. Eastern Cooperative Oncology Group (ECOG) performance status score of 0-2.
5. At least one measurable lesion as defined by Response Criteria in Solid Tumors (RECIST) version 1.1.
6. Life expectancy of at least 6 months.
7. FAP-positive lesion confirmed by FAPI PET/CT scan.
8. Adequate organ function as defined by：
* Bone marrow function: hemoglobin ≥ 100 g/L, neutrophil count ≥ 1.5 × 109/L, platelet count ≥ 100 × 109/L;
* Liver function: albumin ≥ 3.0 g/dL; total bilirubin ≤ 1.5 × ULN; ALT and AST \< 3 × ULN without liver metastasis or \< 5 × ULN with liver metastasis;
* Renal function: creatinine clearance ≥ 60 mL/min.
9. Clinically significant toxic reactions related to prior antitumor treatment that have recovered to Grade ≤ 1 (CTCAE V5.0).
Exclusion Criteria:
1. Known central nervous system metastases, except for the following:
* Subject without clinical symptoms can be included in this trial after evaluation by the investigator.
* Brain metastases that have been previously treated and confirmed by image to be stable for at least 4 weeks.
2. Secondary malignancy was detected within 5 years prior to first dosing, excluding cured localized carcinoma including cervical carcinoma in situ, basal cell skin cancer, and prostate cancer in situ, etc.
3. Received antitumor treatment including chemotherapy, radiotherapy, immunotherapy, and traditional Chinese medicine, etc. within 4 weeks prior to first dosing.
4. Subject who previously received targeted therapy, but discontinued treatment for less than 4 weeks or 10 half-lives prior to first dosing.
5. Received systemic radionuclide therapy or radioembolization within 6 months before first dosing or any external beam radiotherapy within 2 weeks before the first dosing.
6. Known allergy to 177Lu-LNC1004 Injection or similar drugs.
7. Subject has not fully recovered from major surgery prior to first dosing or expects to have major surgery during the study period.
8. Accompanied with severe cardiovascular and cerebrovascular diseases, including but not limited to:
* Subject who has undergone coronary angioplasty, coronary stent placement, coronary artery bypass grafting, or implantation of defibrillation devices due to arrhythmia within 6 months;
* There are serious heart rhythm or conduction abnormalities, such as ventricular arrhythmias requiring clinical intervention, degree II-III atrioventricular block, etc.
* Clinically significant abnormal ECG during the screening period, including QTcF \> 470 ms in male and QTcF \> 480 ms in female.
* New York College of Cardiology (NYHA) grade ≥ 3.
* Aortic dissection, stroke, or other grade 3 or higher cardiovascular and cerebrovascular event (NCI CTCAE v5.0) within 6 months.
9. Subject who has active and clinically significant bacterial, fungal, viral infection, or any other uncontrolled active infections such as active tuberculosis within 4 weeks prior to first dosing.
10. Known human immunodeficiency virus (HIV) infection or positive HIV test, positive syphilis antibody test, or active hepatitis except for:
* Subject who is positive for hepatitis B surface antigen can be enrolled if HBV DNA level is less than 1×104 copies/mL or 2000 IU/mL, and can receive antiviral treatment according to clinical judgment during the trial.
* Subject who is positive for HCV antibodies can be enrolled if HCV RNA test is negative.
11. Previously received allogeneic hematopoietic stem cell transplantation or organ transplantation.
12. Subject who has pleural effusion or ascites that required treatment or is deemed uncontrollable by investigator.
13. Subject who has mental illness or substance abuse, which may affect adherence to the trial.
14. Subject who refuses to take effective contraceptive measures during sexual intercourse from ICF signing to 6 months after last investigational drug administration；
15. Women who are pregnant or breastfeeding, or planning to become pregnant during the study period or within 6 months after last investigational drug administration；
16. Any other medical condition, metabolic abnormality, physical abnormality, laboratory abnormality, or other condition that the investigator deems inappropriate for study participation, or that would affect the interpretation of the study results, or place the subject at high risk, such as idiopathic pulmonary fibrosis or lung disease, urinary incontinence, etc.
