Surgical Debulking Prior to Peptide Receptor Radionuclide Therapy in Well Differentiated Gastroenteropancreatic Neuroendocrine Tumors

Inclusion Criteria: * Signed and dated written informed consent * Male or female \>= 18 years of age on the day of signing informed consent * Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1 or 2 * Histologically confirmed well-differentiated gastrointestinal or pancreatic neuroendocrine tumor that is grade 1 or grade 2 (Ki-67 =\< 20%) * Somatostatin receptor avidity of known or suspected neuroendocrine tumor (NET) lesion(s) assessed by a baseline copper-64 dotatate PET/CT scan performed within 6 months (180 days) prior to surgical debulking on study day 0. The somatostatin receptor avidity of the majority of suspected NET lesion(s) must be \>= normal liver uptake * Patient must have hepatic metastasis or hepatic metastases. Provided required hepatic metastatic disease is present, patient can also have any other site or sites of metastatic disease * White blood cell count (WBC) \>= 2000/uL (resulted =\< 90 days prior to surgical debulking on day 0 of participation in this study) * Platelets \>= 75,000/uL (resulted =\< 90 days prior to surgical debulking on day 0 of participation in this study) * Hemoglobin \>= 8.0 g/dL (resulted =\< 90 days prior to surgical debulking on day 0 of participation in this study) * Creatinine clearance (CrCl) \>= 30 mL/minute (as calculated by the Cockcroft-Gault Formula with estimated creatinine clearance rate \[eCCR\] \>= 30 mL/min required for eligibility inclusion; or calculated/measured by an alternative established institutional standard consistently applied across participants at the site) (resulted =\< 90 days prior to surgical debulking on day 0 of participation in this study) * Total bilirubin =\< 3.0 times institutional upper limit of normal (ULN) (resulted =\< 90 days prior to surgical debulking on day 0 of participation in this study) * Serum albumin \>= 3.0 g/dL unless the prothrombin time is within normal range (resulted =\< 90 days prior to surgical debulking on day 0 of participation in this study) * Women must not be breastfeeding and further agree to not breastfeed during treatment with lutetium Lu 177 dotatate; and for at least 2.5 months after patient's final dose of lutetium Lu 177 dotatate * A woman of childbearing potential (WOCBP) - must have a negative serum or urine pregnancy test resulted within 28 days prior to initiation of first dose of lutetium Lu 177 dotatate on cycle 1, day 1; and must agree to follow instructions for using acceptable contraception from the time of signing consent, and until 7 months after her final dose of lutetium Lu 177 dotatate * A man able to father children who is sexually active with a WOCBP must agree to follow instructions for using acceptable contraception, from the time of signing consent, and until 4 months after his final dose of lutetium Lu 177 dotatate Exclusion Criteria: * Patient has any tumor \> 3 cm deemed to be inoperable * Patient has disease which is considered to be completely surgically resectable * Patient has grade 3 neuroendocrine neoplasm (well-differentiated or poorly-differentiated tumor) * Prior receipt of peptide receptor radionuclide therapy (PRRT) * Patient possesses untreated or growing brain metastases (growth within 90 days prior to surgical debulking on day 0 of participation in this study) * Unstable angina, congestive heart failure with New York Heart Association (NYHA) functional classification III or IV, or uncontrolled symptomatic cardiac arrythmia * Any other significant medical, psychiatric, or surgical condition, currently uncontrolled by treatment, which in the judgment of the patient's study physician may reasonably be expected to interfere with patient's completion of the study