Pevonedistat, Irinotecan, and Temozolomide in Treating Patients With Recurrent or Refractory Solid Tumors or Lymphoma

Inclusion Criteria: * Part A1: Patients must be \>= 12 months and =\< 21 years of age at the time of study enrollment * Part A2: Patients must be \>= 6 months and \< 12 months of age at the time of study enrollment; patients will enroll one dose level behind the dose level at which patients in Part A1 are enrolling * Patients with recurrent or refractory solid tumors, including CNS tumors and lymphoma, for which no standard therapy is available are eligible; patients must have had histologic verification of malignancy at original diagnosis or relapse except in patients with intrinsic brain stem tumors, optic pathway gliomas, or patients with pineal tumors and elevations of cerebrospinal fluid (CSF) or serum tumor markers including alpha-fetoprotein or beta-human chorionic gonadotropin (HCG) * Patients must have either measurable or evaluable disease * Patient's current disease state must be one for which there is no known curative therapy or therapy proven to prolong survival with an acceptable quality of life * Karnofsky \>= 50% for patients \> 16 years of age and Lansky \>= 50 for patients =\< 16 years of age; NOTE: neurologic deficits in patients with CNS tumors must have been relatively stable for at least 7 days prior to study enrollment; patients who are unable to walk because of paralysis, but who are up in a wheelchair, will be considered ambulatory for the purpose of assessing the performance score * Patients must have fully recovered from the acute toxic effects of all prior anti-cancer therapy and must meet the following minimum duration from prior anti-cancer directed therapy prior to enrollment; if after the required time frame, the numerical eligibility criteria are met, e.g. blood count criteria, the patient is considered to have recovered adequately * Cytotoxic chemotherapy or other anti-cancer agents known to be myelosuppressive; at least 21 days after the last dose of cytotoxic or myelosuppressive chemotherapy (42 days if prior nitrosourea); the duration of this interval must be discussed with the study chair and the study-assigned research coordinator prior to enrollment * Anti-cancer agents not known to be myelosuppressive (e.g. not associated with reduced platelet or absolute neutrophil counts \[ANC\] counts): \>= 7 days after the last dose of agent; the duration of this interval must be discussed with the study chair and the study-assigned research coordinator prior to enrollment * Antibodies: \>= 21 days must have elapsed from infusion of last dose of antibody, and toxicity related to prior antibody therapy must be recovered to grade =\< 1 * Corticosteroids: if used to modify immune adverse events related to prior therapy, \>= 14 days must have elapsed since last dose of corticosteroid * Hematopoietic growth factors: \>= 14 days after the last dose of a long-acting growth factor (e.g. pegfilgrastim) or 7 days for short-acting growth factor; for agents that have known adverse events occurring beyond 7 days after administration, this period must be extended beyond the time during which adverse events are known to occur; the duration of this interval must be discussed with the study chair and the study-assigned research coordinator * Interleukins, interferons and cytokines (other than hematopoietic growth factors): \>= 21 days after the completion of interleukins, interferon or cytokines (other than hematopoietic growth factors) * Stem cell Infusions (with or without total body irradiation \[TBI\]): * Allogeneic (non-autologous) bone marrow or stem cell transplant, or any stem cell infusion including donor lymphocyte infusion (DLI) or boost infusion: \>= 84 days after infusion and no evidence of graft versus host disease (GVHD) * Autologous stem cell infusion including boost infusion: \>= 42 days * Cellular therapy: \>= 42 days after the completion of any type of cellular therapy (e.g. modified T cells, natural killer \[NK\] cells, dendritic cells, etc.) * Radiation therapy (XRT)/external beam irradiation including protons: \>= 14 days after local XRT; \>= 150 days after TBI, craniospinal XRT or if radiation to \>= 50% of the pelvis; \>= 42 days if other substantial brain metastases (BM) radiation * Radiopharmaceutical therapy (e.g., radiolabeled antibody, 131I-metaiodobenzylguanidine \[MIBG\]): \>= 42 days after systemically administered radiopharmaceutical therapy * Patients must not have received prior exposure to pevonedistat; patients with prior exposure to irinotecan or temozolomide are eligible * For patients with solid tumors without known bone marrow involvement: * Peripheral absolute neutrophil count (ANC) \>= 1000/mm\^3 * Platelet count \>= 100,000/mm\^3 (transfusion independent, defined as not receiving platelet transfusions for at least 7 days prior to enrollment) * Hemoglobin \>= 8 g/dL * Patients with known bone marrow metastatic disease will be eligible for study provided they meet the blood counts (may receive transfusions provided they are not known to be refractory to red cell or platelet transfusions); these patients will not be evaluable for hematologic toxicity; at least 5 of every cohort of 6 patients on Part A1 must be evaluable for hematologic toxicity for the dose-escalation part of the study; if dose-limiting hematologic toxicity is observed, all subsequent patients enrolled must be evaluable for hematologic toxicity * Creatinine clearance or radioisotope glomerular filtration rate (GFR) \>= 70 mL/min/1.73 m\^2 or a serum creatinine based on age/gender as follows: * Age: 6 months to \< 1 years maximum serum creatinine (mg/dL): male: 0.5; female: 0.5 * Age: 1 to \< 2 years maximum serum creatinine (mg/dL): male: 0.6; female: 0.6 * Age: 2 to \< 6 years maximum serum creatinine (mg/dL): male: 0.8; female: 0.8 * Age: 6 to \< 10 years maximum serum creatinine (mg/dL): male: 1; female: 1 * Age: 10 to \< 13 years maximum serum creatinine: (mg/dL): male: 1.2; female: 1.2 * Age: 13 to \< 16 years maximum serum creatinine: (mg/dL): male: 1.5; female: 1.4 * Age: \>= 16 years maximum serum creatinine: (mg/dL) male: 1.7; female: 1.4 * Bilirubin (sum of conjugated + unconjugated) =\< upper limit of normal (ULN) for age * Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransaminase \[ALT\]) =\< 135 U/L; for the purpose of this study, the ULN for SGPT is 45 U/L * Serum glutamic-oxaloacetic transaminase (SGOT) (aspartate aminotransferase) \[AST\]); =\< 150 U/L; for the purpose of this study, the ULN for SGOT is 50 U/L * Serum albumin \>= 2.7 g/dL * Shortening fraction of \>= 27% by echocardiogram, or * Ejection fraction of \>= 50% by gated radionuclide study * No supraventricular arrhythmia on electrocardiogram (EKG) * Prolonged rate corrected QT (QTc) interval \< 500 msec * Pulse oximetry \> 94% on room air if there is clinical indication for determination (e.g. dyspnea at rest) * Patients with seizure disorder may be enrolled if on non-enzyme inducing anti-convulsants and well controlled * Nervous system disorders (Common Terminology Criteria for Adverse Events \[CTCAE\] version 5.0) resulting from prior therapy must be =\< grade 2, with the exception of decreased tendon reflex (DTR); any grade of DTR is eligible * International normalized ratio (INR) =\< 1.5 * All patients and/or their parents or legally authorized representatives must sign a written informed consent; assent, when appropriate, will be obtained according to institutional guidelines Exclusion Criteria: * Pregnant or breast-feeding women will not be entered on this study because there is not yet available information regarding human fetal or teratogenic toxicities; pregnancy tests must be obtained in girls who are post-menarchal * Males or females of reproductive potential may not participate unless they have agreed to practice 1 highly effective and 1 additional effective (barrier) method of contraception at the same time during the entire study treatment period and through 4 months after the last dose of study drug, or agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the subject; periodic abstinence (e.g., calendar, ovulation, symptothermal, post-ovulation methods), withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception * Patients with uncontrolled high blood pressure (i.e., systolic/diastolic blood pressure \> 99th percentile) are not eligible * Patients with known cardiopulmonary disease are not eligible; cardiopulmonary disease is defined as: * Cardiomyopathy other than chemotherapy related changes in cardiac function that meet the eligibility requirements * Clinically significant arrhythmia: * History of polymorphic ventricular fibrillation or torsade de pointes, * Permanent atrial fibrillation (a fib), defined as continuous a fib for \>= 6 months, * Persistent a fib, defined as sustained a fib lasting \> 7 days and/or requiring cardioversion in the 4 weeks before screening, * Grade 3 a fib defined as symptomatic and incompletely controlled medically, or controlled with device (e.g. pacemaker), or ablation and * Patients with paroxysmal a fib or \< grade (Gr) 3 a fib for period of at least 6 months are permitted to enroll provided that their rate is controlled on a stable regimen * Implantable cardioverter defibrillator; * Moderate to severe aortic and/or mitral stenosis or other valvulopathy (ongoing); * Pulmonary hypertension * Congestive heart failure class III or IV * Patients with known hepatic cirrhosis or severe pre-existing hepatic impairment are not eligible * Patients with uncontrolled coagulopathy or bleeding disorder are not eligible * Patients receiving corticosteroids who have not been on a stable or decreasing dose of corticosteroid for at least 7 days prior to enrollment are not eligible; if used to modify immune adverse events related to prior therapy, \>= 14 days must have elapsed since last dose of corticosteroid * Patients who are currently receiving another investigational drug are not eligible * Patients who are currently receiving other anti-cancer agents are not eligible * Patients must not have received enzyme-inducing anticonvulsants for at least 7 days prior to enrollment * Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial * Patients who are receiving any investigational agent other than pevonedistat, including but not limited to androgens, supraphysiologic doses of corticosteroids, erythropoietin, eltrombopag, or romiplostim * Patients who have received drugs that are strong inducers of CYP3A4 within 14 days prior to study enrollment are not eligible; while on study, concomitant use of strong CYP3A4 inhibitors, BCRP inhibitors (cyclosporine, eltrombopag, gefitinib), and UGT1A1 inhibitors, (diclofenac, ketoconazole, probenecid, silibinin, nilotinib and atazanavir) should be avoided because of potential for increased irinotecan toxicity * Patients who have an uncontrolled infection are not eligible * Patients who have received a prior solid organ transplantation are not eligible * Patients with known human immunodeficiency virus (HIV) seropositive are not eligible * Patients with known hepatitis B surface antigen seropositive or known or suspected active hepatitis C infection are not eligible; NOTE: patients who have isolated positive hepatitis B core antibody (i.e., in the setting of negative hepatitis B surface antigen and negative hepatitis B surface antibody) must have an undetectable hepatitis B viral load; patients who have positive hepatitis C antibody may be included if they have an undetectable hepatitis C viral load * History of allergic reactions attributed to compounds of similar chemical or biologic composition as the study agents * Patients who in the opinion of the investigator may not be able to comply with the safety monitoring requirements of the study are not eligible