Testing the Safety of M6620 (VX-970) When Given With Standard Whole Brain Radiation Therapy for the Treatment of Brain Metastases From Non-small Cell Lung Cancer, Small Cell Lung Cancer, or Neuroendocrine Tumors

Inclusion Criteria: * Patients with a histologically confirmed diagnosis of non-small cell lung cancer (NSCLC), including neuroendocrine tumors or small cell lung cancer (SCLC) who are being evaluated for palliative WBRT (with or without neurosurgical resection or stereotactic radiosurgery \[SRS\]) for radiologically or histologically diagnosed brain metastases presumed to be from the lung cancer are eligible for this Phase I study. Group 2 will only include NSCLC patients. * Life expectance of greater than two months to allow completion of study treatment and assessment of dose-limiting toxicity * Group 2 patients should have archived or fresh tumor tissue available from the non-craniotomy site and will have fresh tumor tissue available from the planned craniotomy * Age \>= 18 years. Because no dosing or adverse event data are currently available on the use of M6620 (VX-970, berzosertib) in patients \< 18 years of age, children are excluded from this study, but will be eligible for future pediatric trials. * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Note: though patients with ECOG performance status of 3 due to neurological deficits who are otherwise fit to receive systemic therapy per clinician assessments will be allowed * Leukocytes \>= 3,000/mcL * Absolute neutrophil count (ANC) \>= 1,500/mcL * Platelets \>= 100,000/mcL * If no known liver metastases: total bilirubin \< 1.5 x institutional upper limit of normal (ULN); if known liver metastases, then: total bilirubin \< 2.5 x ULN * If no known liver metastases: aspartate aminotransferase (AST)/serum glutamic oxaloacetic transaminase (SGOT) or alanine aminotransferase (ALT)/serum glutamic pyruvic transaminase (SGPT) \< 2 x ULN; if known liver metastases, then: AST/SGOT of ALT/SGPT \< 5 x ULN * Creatinine within normal institutional limits for age OR creatinine clearance \>= 45 mL/min/1.73 m\^2 for patients with creatinine levels above ULN * Negative serum or urine pregnancy test result for females of child bearing potential * The effects of M6620 (VX-970, berzosertib) on the developing human fetus are unknown. For this reason and because radiation therapy is known to have teratogenic potential, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 6 months after completion of M6620 (VX-970, berzosertib) administration. * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients with 1-3 brain metastases, each \< 3 cm by contrast MRI, with stable systemic disease and ECOG score of 0-2, who would otherwise be eligible for SRS/stereotactic radiation therapy (SRT) alone should not be enrolled into this study unless WBRT is recommended due to any medical reasons or logistic limitations as determined by the treating physician. Patients who develop recurrence post-SRS/SRT or surgery alone and are recommended WBRT will be eligible for the protocol. * Greater than 1 cm mid-line shift, severe uncal herniation or significant hemorrhage/hydrocephalus (intra-lesional hemorrhage is acceptable). Patients with seizure at presentation who have been started on levetiracetam and have been stable for 48 hours prior to study registration are eligible at the discretion of treating physician * Patients who have received systemic cytotoxic chemotherapy and/or, immunotherapy or other intravenous standard therapy for 2 weeks before initiation of planned WBRT, for oral targeted agents 3-7 days per clinician discretion or patients who have not recovered to Common Terminology Criteria for Adverse Events (CTCAE) grade 2 or less from serious (CTCAE grade 3 or more) adverse events form the previously received agents. For any other investigational agents, at least 4 half-lives of the agent (6 weeks for nitrosoureas or mitomycin C) should have elapsed prior to starting study treatment * Patients must not have received prior WBRT (previous SRS/SRT done at least 2 weeks from the planned start of WBRT is acceptable). Patients planned upfront to undergo SRS/SRT/fractionated boosts or neurosurgery after WBRT are not eligible; however, these treatments/procedures can be performed once the dose limiting toxicity (DLT) assessment has been completed, if felt clinically necessary * Pregnant women are excluded from this study because M6620 (VX-970, berzosertib) as a deoxyribonucleic acid (DNA)-damage response (DDR) inhibitor may have the potential for teratogenic or abortifacient effects. Further, radiation therapy is known to have 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 M6620 (VX-970, berzosertib), breastfeeding should be discontinued if the mother is treated with M6620 (VX-970, berzosertib). * History of allergic reactions attributed to compounds of similar chemical or biologic composition to M6620 (VX-970, berzosertib). * M6620 (VX-970, berzosertib) is primarily metabolized by cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4); therefore, concomitant administration with strong inhibitors or inducers of CYP3A4 should be avoided. Because the lists of these agents are constantly changing, it is important to regularly consult a frequently-updated medical reference for a list of drugs to avoid or minimize use of. 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. Ongoing phenytoin should be either discontinued if clinically safe or transitioned to non-enzyme-inducing antiepileptics like levetiracetam with a 8-day washout period (half-life 18-22 hours, time to steady-state 4-8 days) prior to first dose of M6620 (VX-970, berzosertib) (7-days prior to WBRT). * Patients needing more than 8 mg dexamethasone per day at the time of start of WBRT will not be eligible to participate in the study. However, patients will be allowed entry into the study if it is medically safe to reduce the daily dose of dexamethasone to 8 mg or less from the day of the start of WBRT. The dexamethasone dose for such patients may be increased beyond 8 mg per day during the course of treatment if medically necessary. This increased need for dose should be communicated to the study's principal investigator, Dr Mohindra at the University of Maryland. * Uncontrolled intercurrent illness that would increase the risk of toxicity or limit compliance with study requirements. This includes but is not limited to, ongoing uncontrolled serious infection requiring i.v. antibiotics at the time of registration, or psychiatric illness/social situations that would limit compliance with study requirements * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with M6620 (VX-970, berzosertib) and the uncertainties of any impact thereof on the radiation toxicities. In addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy. Appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated. * Patients with known diagnoses that are associated with germline DDR defects such as Li Fraumeni syndrome and ataxia telangiectasia are excluded from the study as M6620 (VX-970, berzosertib) is a DDR inhibitor.