Testing the Effectiveness of an Anti-cancer Drug, Triapine, When Used With Targeted Radiation-based Treatment (Lutetium Lu 177 Dotatate), Compared to Lutetium Lu 177 Dotatate Alone for Metastatic Neuroendocrine Tumors

Inclusion Criteria:

* Patients must have metastatic, histologically confirmed well-differentiated neuroendocrine tumor with positive gallium 68 DOTATATE or copper 64 DOTATATE scan. Lesions on dotatate scan will be considered positive if the standardized uptake value maximum (SUVmax) of target lesion is \> 2 times standardized uptake value (SUV) mean of normal liver parenchyma. Patients with lung neuroendocrine tumors (NETs) are excluded from the trial
* Patients must have progressive disease based on RECIST criteria, version 1.1 evidenced with CT scans/MRI obtained within 24 months from enrollment
* Patients must have measurable disease per RECIST 1.1
* Failure of at least one prior systemic cancer treatment with somatostatin analogs
* No prior exposure to peptide receptor radionuclide therapy
* Recovered from adverse events of previously administered therapeutic agents (i.e., to grade 2 or less toxicity) according to Common Terminology Criteria for Adverse Events (CTCAE) 5.0
* Age \>= 18 years

  * Because no dosing or adverse event data are currently available on the use of triapine in combination with lutetium Lu 177 dotatate in patients \< 18 years of age, children are excluded from this study
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%)
* Absolute neutrophil count \>= 1,500/mcL
* Platelets \>= 100,000/mcL
* Total bilirubin =\< 1.5 institutional upper limit of normal (ULN)
* Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x institutional ULN
* Serum creatinine =\< 1.5 institutional ULN. Creatinine \> 1.5 ULN will require a measured creatinine clearance (CrCl) \> 50 ml/min to qualify
* Hemoglobin \> 5.0 mmol/L (\> 8.0 g/dL)
* Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial
* For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated
* Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load
* Patients with treated brain metastases and off steroids are eligible if follow-up brain imaging after central nervous system (CNS)-directed therapy shows no evidence of progression for at least 4 weeks prior to enrollment in the study. Patients with a history of brain metastases must have a head CT with contrast to document stable disease prior to enrollment in the study
* Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial
* Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2B or better
* Pregnancy precaution: Men and women should avoid pregnancy for seven months after the date of their last treatment with lutetium Lu 177 dotatate. It is noteworthy that beta-human chorionic gonadotropin (beta-HCG) may be secreted by a small percentage of NETs, such that, in addition to being a pregnancy marker, it also is a tumor marker. Consequently, NET female patients with positive beta-HCG (\> 5 mIU/mL) at baseline can be eligible to enter the study and receive treatment if pregnancy can be excluded by lack of expected doubling of beta-HCG and negative pelvic ultrasound. Normally, in pregnant subjects beta-HCG doubles every 2 days during the first 4 weeks of pregnancy and every 3.5 days by weeks 6 to 7. Women of childbearing potential include any female who has experienced menarche and who has not undergone successful surgical sterilization (hysterectomy, bilateral tubal ligation, or bilateral ovariectomy) or is not postmenopausal (defined as amenorrhea \> 12 consecutive months, and for women on hormone replacement therapy, only with a documented plasma follicle-stimulating hormone \[FSH\] level \> 35 mIU/mL). Even women who are using oral, implanted, or injected contraceptive hormones, an intrauterine device (IUD), or barrier methods (diaphragm, condoms, spermicidal) to prevent pregnancy, are practicing abstinence or where the partner is sterile (e.g., vasectomy) should be considered to be of childbearing potential. Postmenopausal women who have fertilized eggs implanted are also considered to be of childbearing potential. Acceptable methods of contraception may include total abstinence at the discretion of the Investigator in cases where the age, career, lifestyle, or sexual orientation of the patient ensures compliance. Periodic abstinence (e.g., calendar, ovulation, symptothermal, post-ovulation methods) and withdrawal are not acceptable methods of contraception. Reliable contraception (hormonal or barrier method of birth control; abstinence) should be maintained throughout the study and for 7 months after study treatment discontinuation. All men and women of childbearing potential and male partners must use a double-barrier method of birth control or practice continuous abstinence from heterosexual contact throughout the study and for seven months after the end of the last treatment
* Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

* Patients who have not recovered from adverse events of previously administered therapeutic agents (i.e., have residual toxicities \> grade 2) according to CTCAE 5.0, with the exception of alopecia
* Patients who are receiving any other investigational agents
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to triapine or lutetium Lu 177 dotatate
* Patients with uncontrolled intercurrent illness
* Uncontrolled congestive heart failure (New York Heart Association \[NYHA\] III, IV)
* Pregnant women are excluded from this study because triapine is a ribonucleotide reductase (RNR) inhibitor and lutetium Lu 177 dotatate is a peptide receptor radionuclide therapy with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with triapine and lutetium Lu 177 dotatate, breastfeeding should be discontinued if the mother is treated with triapine and lutetium Lu 177 dotatate and for 2.5 months following the last treatment
* Inability to swallow oral medications or gastrointestinal disease limiting absorption of oral agents
* Patients with any other significant condition, currently uncontrolled by treatment, which may interfere with completion of the study