177Lu-DOTA-EB-TATE in Adult Patients With Metastatic, Radioactive Iodine Non-Responsive Oncocytic (Hurthle-Cell) Thyroid Cancer

* INCLUSION CRITERIA: In order to be eligible to participate in this study, an individual must meet all of the following criteria: * Aged 18 years or older. * Metastatic RAI-non-responsive and/or RAI-non-avid oncocytic (Hurthle cell) thyroid cancer. * Progressive disease by RECIST 1.1 criteria, with or without symptoms within the last 12 months. This applies to patients with non-measurable disease by RECIST 1.1 criteria, who will be eligible if they have evidence of progression as defined by the development of new lesions within the last 12 months. * High expression of SSTR2 in at least one metastatic lesion as documented by 68Ga-DOTATATE PET/CT with SUVmax \> SUVmax of the liver consistent with Krenning score of \>2 or SUVmax \>= 13 based on scan performed within 12 weeks of anticipated enrollment. EXCLUSION CRITERIA: An individual who meets any of the following criteria will be excluded from participation in this study: * Pregnant or breastfeeding. * NET/PET score of 5 by imaging with 68Ga-DOTATATE PET/CT and 18FDG-PET/CT and defined more than 2 lesions that are SSTR2 negative but 18FDG positive and/or more than 2 lesions that have significantly higher uptake of 18FDG than 68Ga-DOTATATE * History of allergic reactions attributed to compounds of similar chemical or biologic composition to 177Lu-DOTA-EB-TATE as assessed from medical record. * Patient weight \> 500 lbs. (due to the PET scanner table limit). * Inability to tolerate at least one modality of diagnostic anatomic imaging, such as CT or MRI. * Participant has had prior chemotherapy, targeted cancer therapy, immunotherapy, or treatment with an investigational anticancer agent within 4 weeks or 4 half-lives (whichever is longer), before the first administration of study drug. * Previous surgery \< 6 weeks prior to the start of participation in this study, or participant has not fully recovered from major surgery, or has suffered significant traumatic injury prior 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 \< 6 months as assessed by the treating physician. * Karnofsky performance status scale \< 70%. * Inability or unwillingness to use adequate contraception prior to study entry and for the duration of study participation, including follow-up (7 months after the last dose of study drug for women and 4 months for men). The adequate contraception consists of intrauterine device, contraceptive implant, hormonal contraception or a double-barrier method. If the patient is status post tubal ligation, status post hysterectomy and/or oophorectomy, or their male partners are status post vasectomy, no additional method of contraception is required. * Deteriorated renal function, as indicated by a creatinine clearance \<60 mL/min calculated by the Cockcroft-Gault Equation. The calculated creatinine clearance can be confirmed by measured creatinine clearance. * Having only one functional kidney, due to potential nephrotoxicity. * Patients who have had any prior EBRT dose to either kidney. * Deteriorated bone marrow function, as indicated by: * Hemoglobin (Hb) \< 8.0 g/dL * White blood cell (WBC) \< 2 x10\^3/uL * Absolute neutrophil count (ANC) \< 1.0 x 10\^3/L * Platelets \<100 x 10\^3/microL * Deteriorated liver function, as indicated by one or more of the following: * International normalized ratio (INR) \> 2.0 for patients that are not on Coumadin * Prothrombin time (PTT) \> 2 x ULN * Total bilirubin \> 3 mg/dL * Serum albumin \< 3.0 g/dL unless prothrombin time is within the normal range * Alanine aminotransferase (ALT) \> 3 x ULN * Aspartate aminotransferase (AST) \> 3 x ULN. * Previous local therapy \<4 weeks prior to study entry. * Extended QTc interval above 480 ms confirmed by 2 ECGs. If the first ECG conducted at the screening visit shows extended QTc interval, potential participants will be asked to repeat an ECG within 30 days to confirm. The second ECG can be conducted at NIH CC or at their outside provider, at their potential expense. * Toxicities from prior therapies that have not resolved to grade 1 or grade 0 excluding dry mouth syndrome from previous RAI and grade 2 anemia/leukopenia as Hgb\>=8 g/dl, WBC \>=2 x10\^3/uL and ANC \>= 1.0 x 10\^3 are acceptable for enrollment. * Active and clinically significant bacterial, fungal, or viral infection, including hepatitis B (HBV), hepatitis C (HCV), known human immunodeficiency virus (HIV), or acquired immunodeficiency syndrome (AIDS)-related illness. Radiolabeled ligands may affect the immune response, so people with active and clinically significant infections may become too immunocompromised through participation in this study. * Known brain metastases and/or carcinomatous meningitis unless these metastases have been treated and stabilized. * Uncontrolled, intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Prior external beam radiation therapy involving \>25% of the bone marrow. * Unmanageable urinary incontinence rendering the administration of 177Lu-DOTA-EB-TATE unsafe. * Other known co-existing malignancies except non-melanoma skin cancer and carcinoma in situ of the uterine cervix, unless definitively treated and with no evidence of recurrence. * Is unwilling or unable to establish care with a local provider outside of NIH CC * Inability to understand or unwilling to sign a written informed consent document.