Testing the Addition of An Anti-cancer Drug, M3814 (Peposertib), to the Usual Radiation-Based Treatment (Lutetium Lu 177 Dotatate) for Pancreatic Neuroendocrine Tumors

Inclusion Criteria:

* Patients must have histologically or cytologically confirmed well-differentiated neuroendocrine tumor with positive dotatate scan (gallium 68 or copper 64) (as determined by the site principal investigator \[PI\]) within 6 months before enrollment. Lesions on the dotatate scan (gallium 68 or copper 64) are considered positive if the maximum standard uptake value (SUVmax) is \> 2 times the mean standard uptake value (SUVmean) of normal liver parenchyma. Patients must have the gallium 68 or copper 64 dotatate scans available to send for central review before enrollment
* Patients must have measurable progressive disease based on RECIST criteria, version 1.1, evidenced with CT/MRI scans obtained within 12 months before enrollment
* Failure of at least one prior systemic cancer treatment with somatostatin analogs
* No prior exposure to peptide receptor radionuclide therapy
* Age \>= 18 years
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%)
* White blood cell count \>= 2,000/mcL
* Absolute neutrophil count \>= 1,000/mcL
* Platelets \>= 75,000/mcL
* Hemoglobin \>= 8.0 g/dL
* Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN)
* Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) =\< 3 x institutional ULN
* Alkaline phosphatase =\< 3 x institutional ULN
* Glomerular filtration rate (GFR) \>= 50 mL/min/1.73 m\^2 (per the Cockcroft-Gault \[C-G\])
* 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 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
* Patients must have recovered from adverse events of previously administered therapeutic agents to grade 2 or less toxicity according to Common Terminology Criteria for Adverse Events (CTCAE) 5.0
* Pregnancy Precaution: Women should avoid pregnancy for seven months after the date of their last treatment with lutetium Lu 177 dotatate. Men should avoid fathering a child for 4 months after the last dose of Lutetium Lu 177 dotatate. It is noteworthy that beta-human chorionic gonadotropin (HCG) may be secreted by a small percentage of neuroendocrine tumor (NET)s, 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, for women, and for 4 months for men. All 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 for women, and four months for men
* Ability to understand and the willingness to sign a written informed consent document. Participants with impaired decision-making capacity (IDMC) who have a legally-authorized representative (LAR) and/or family member available will also be eligible.

Exclusion Criteria:

* Patients who have had major surgical procedures in the 4 weeks prior to enrollment
* Patients are excluded if they received prior systemic peptide receptor radionuclide therapy (PRRT)-based therapies
* Patients with an inability to swallow oral medications or gastrointestinal disease limiting absorption of oral agents
* Patients who are receiving any other investigational agents
* Known brain metastases, unless these metastases have been treated and stabilized for at least 4 weeks, prior to enrollment in the study. Patients with a history of brain metastases must have either a head CT with contrast or brain MRI to document stable disease prior to enrollment in the study
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to M3814 (peposertib) or lutetium Lu 177 dotatate
* Prior external beam radiotherapy to more than 50% of bone marrow (whole body) will be excluded, as determined by a radiation medicine physicist who will calculate the volume of bone marrow exposure in prior radiotherapy portals divided by the volume of total bone marrow harboring tissues. This ratio must be less than 50 percent
* Patients who cannot discontinue concomitant medications or herbal supplements that are strong inhibitors or strong inducers of cytochrome P450 (CYP) isoenzymes CYP3A4/5, CYP2C9, and CYP2C19. Concomitant use of CYP3A4/5, 1A2, 2B6, 2C8, substrates with a narrow therapeutic index are also excluded. Patients may confer with the study doctor to determine if alternative medications can be used. The following categories of medications and herbal supplements must be discontinued for at least the specified period of time before the patient can be treated:

  * Strong inducers of CYP3A4/5, CYP2C9 and CYP2C19: \>= 3 weeks prior to study treatment
  * Strong inhibitors of CYP3A4/5, CYP2C9 and CYP2C19: \>= 1 week prior to study treatment
  * Substrates of CYP3A4/5, 1A2, 2B6, 2C8, with a narrow therapeutic index: \>= 1 day prior to study treatment Because the lists of these agents are constantly changing, it is important to regularly consult a frequently-updated medical reference. As part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product
* Patients who cannot discontinue concomitant proton-pump inhibitors (PPIs). Patients may confer with the study doctor to determine if such medications can be discontinued. These must be discontinued \>= 5 days prior to study treatment. Patients do not need to discontinue calcium carbonate
* Patients with ongoing active infection or treatment with a live attenuated vaccine within 4 weeks of dosing. In addition, a negative polymerase chain reaction (PCR) test for Covid-19 infection is highly recommended before entering the study, and a close symptom follow up within the study
* Patients with uncontrolled intercurrent illness
* Patients with psychiatric illness/social situations that would limit compliance with study requirements
* Pregnant women are excluded from this study because M3814 (peposertib) is a DNA-PK 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 M3814 (peposertib) and lutetium Lu 177 dotatate, breastfeeding should be discontinued if the mother is treated with M3814 (peposertib) and lutetium Lu 177 dotatate and for 2.5 months following the last lutetium Lu 177 dotatate treatment
* Discontinue long-acting somatostatin analogs (e.g., long-acting octreotide) for at least 4 weeks prior to initiating lutetium Lu 177 dotatate. Long-acting somatostatin analogs will be allowed to continue if patient has a history of carcinoid syndrome and requires long-acting somatostatin analogs for control of his/her functional syndrome