Pevonedistat and Ibrutinib in Treating Participants With Relapsed or Refractory CLL or Non-Hodgkin Lymphoma

Inclusion Criteria: * Dose escalation cohort: * Histologically or flow cytometry confirmed diagnosis of B-CLL/small lymphocytic lymphoma (SLL) according to National Cancer Institute sponsored Working Group (NCI-WG) 1996 guidelines * The following types of NHL as documented by medical records and with histology based on criteria established by the World Health Organization (WHO): * Mantle cell lymphoma (MCL) * Follicular lymphoma (FL) - grades 1-3a * Lymphoplasmacytic lymphoma (LPL) * Marginal zone lymphoma (MZL) * CLL in Richter's transformation * B-cell prolymphocytic leukemia (B-PLL) * Diffuse large B-cell lymphoma (DLBCL) * Expansion cohort - histologically or flow cytometry confirmed diagnosis of B-CLL/SLL according to NCI-WG 1996 guidelines; patients who lack CD23 expression on their leukemia cells should be examined for (and found NOT to have) either t(11;14) or cyclin D1 overexpression, to rule out mantle cell lymphoma * Patients with MCL underwent \>= 1 chemoimmunotherapy-based regimen; patients with FL and MZL underwent \>= 1 prior chemotherapy-based and/or immunotherapy-based regimen; patients with DLBCL and CLL in Richter's transformation underwent \>= 1 chemoimmunotherapy-based regimen and are not transplant-eligible; patients with CLL, B-PLL and LPL underwent \>= 1 chemotherapy-based, or immunotherapy-based or targeted therapy regimen (e.g., PI3K inhibitors \[idelalisib\], venetoclax, ibrutinib or an investigational agent, including an investigational BTK inhibitor); all regimens must have been administered for \>= 2 cycles, and patients must have had either documented disease progression or no response (stable disease) to the most recent treatment regimen * Patients with CLL/SLL demonstrate active disease meeting at least 1 of the International Workshop on Chronic Lymphocytic Leukemia (IWCLL) 2008 criteria for requiring treatment: * A minimum of any one of the following constitutional symptoms: * Unintentional weight loss \> 10% within the previous 6 months prior to screening * Extreme fatigue (unable to work or perform usual activities) * Fevers of greater than 100.5 F for \>= 2 weeks without evidence of infection * Night sweats without evidence of infection * Evidence of progressive marrow failure as manifested by the development of, or worsening of anemia or thrombocytopenia * Massive (i.e., \> 6 cm below the left costal margin), progressive or symptomatic splenomegaly * Massive nodes or clusters (i.e., \> 10 cm in longest diameter) or progressive lymphadenopathy * Progressive lymphocytosis with an increase of \> 50% over a 2-month period, or an anticipated doubling time of less than 6 months * Autoimmune anemia or thrombocytopenia that is poorly responsive to corticosteroids * Patients with NHL and with B-cell prolymphocytic leukemia must have an indication for treatment in the opinion of the investigator * For diseases other than LPL and CLL, presence of radiographically measurable lymphadenopathy or extra-nodal lymphoid malignancy (defined as the presence of \>= 1 lesion that measures \>= 2.0 cm in the longest dimension \[LD\] and \>= 1.0 cm in the longest perpendicular dimension \[LPD\] as assessed by computed tomography \[CT\] or magnetic resonance imaging \[MRI\]); for LPL, measurable disease will be defined as serum monoclonal IgM \> 0.5 g/dL or meeting at least 1 of the recommendations from the Second International Workshop on LPL for requiring treatment * Patients must have Eastern Cooperative Oncology Group (ECOG) performance status 0-2 and expected survival \> 3 months from study enrollment * Total bilirubin =\< institutional upper limit of normal (ULN) (unless due to known Gilbert's syndrome or compensated hemolysis directly attributable to CLL); patients with Gilbert's syndrome may enroll if direct bilirubin =\< 1.5 x ULN of the direct bilirubin; elevated indirect bilirubin due to post-transfusion hemolysis is allowed * Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) less than 2.5 X institutional ULN * Estimated creatinine clearance (CrCL) using the Cockcroft-Gault equation \>= 50 mL/min * Platelets \>= 50,000/mm\^3 independent of transfusion support, with no active bleeding, and absolute neutrophil count \>= 1000/mm\^3, unless due to disease involvement in the bone marrow * Albumin \> 2.7 g/dL * Hemoglobin \> 8 g/dL; patients may be transfused to achieve this value * Voluntary written consent must be given before performance of any study related procedure not part of standard medical care, with the understanding that consent may be withdrawn by the patient at any time without prejudice to future medical care * Female patients who: * Are postmenopausal for at least 1 year before the screening visit, OR * Are surgically sterile, OR * If they are of childbearing potential: * Agree to practice 1 highly effective method and 1 additional effective (barrier) method of contraception at the same time, from the time of signing the informed consent 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 \[eg, calendar, ovulation, symptothermal, post-ovulation methods\] withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception; female and male condoms should not be used together) * Male patients, even if surgically sterilized (i.e., status post-vasectomy), who: * Agree to practice effective barrier contraception 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 \[e.g., calendar, ovulation, symptothermal, post-ovulation methods for the female partner\] withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception; female and male condoms should not be used together) Exclusion Criteria: * Prior therapeutic intervention with any of the following: * Therapeutic anticancer antibodies (rituximab, obinutuzumab) within 4 weeks * Radio- or toxin-immunoconjugates within 10 weeks * Inhibitors of PI3K (idelalisib), ibrutinib, BH3-mimetic venetoclax, lenalidomide, and other targeted therapy (including investigational BTK inhibitors and other investigational therapy) within 6 half-lives * All other chemotherapy, radiation therapy within 3 weeks prior to initiation of therapy * Intolerance of ibrutinib * Inadequate recovery from adverse events related to prior therapy to grade =\< 1 (excluding grade 2 alopecia and neuropathy) * Chronic use of corticosteroids in excess of prednisone 20 mg/day or its equivalent * Stem cell transplant recipients must have no evidence of active graft-versus-host disease and should not be receiving treatment for it * Known involvement of central nervous system * Use of full dose, therapeutic anti-coagulation or patients with uncontrolled coagulopathy or bleeding disorder * Treatment with strong CYP3A inhibitors or inducers within 14 days before the first dose of study drug; strong CYP3A inhibitors/inducers are not permitted during the study, including nutraceutical preparations, e.g., grapefruit juice and St John's wort; patients must have no prior history of amiodarone in the 6 months prior to the first dose of pevonedistat * Patient requiring chronic treatment with BCRP inhibitors (cyclosporine, eltrombopag) * History prior malignancy except: * Malignancy treated with curative intent and no known active disease present for \>= 2 years prior to initiation of therapy on current study * Adequately treated non-melanoma skin cancer or lentigo maligna (melanoma in situ) without evidence of disease * Adequately treated in situ carcinomas (e.g., cervical, esophageal, etc.) without evidence of disease * Asymptomatic prostate cancer managed with watch and wait strategy * Myelodysplastic syndrome which is clinically well controlled and no evidence of the cytogenetic abnormalities characteristic of myelodysplasia on the bone marrow at screening * Uncontrolled immune hemolysis or thrombocytopenia (positive direct antiglobulin test in absence of hemolysis or history of immune-mediated cytopenias are not exclusions) * History of human immunodeficiency virus (HIV) infection * Known hepatitis B surface antigen seropositive or known or suspected active hepatitis C Infection; 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 * Known cardiopulmonary disease defined as one of the following: * Unstable angina * Uncontrolled high blood pressure (ie, systolic blood pressure \> 180 mmHg, diastolic blood pressure \> 95 mm Hg ) * Congestive heart failure (New York Heart Association \[NYHA\] class III or IV) * Myocardial infarction (MI) within 6 months prior to first dose (patients who had ischemic heart disease such as a (acute chest syndrome \[ACS\]), MI, and/or revascularization greater than 6 months before screening and who are without cardiac symptoms may enroll) * Cardiomyopathy * Clinically significant arrhythmia: 1) History of polymorphic ventricular fibrillation or torsade de pointes, 2) Permanent atrial fibrillation \[a fib\], defined as continuous a fib for \>= 6 months, 3) Persistent a fib, defined as sustained a fib lasting \> 7 days and/or requiring cardioversion in the 4 weeks before screening, 4) grade 3 a fib defined as symptomatic and incompletely controlled medically, or controlled with device (e.g. pacemaker), or ablation and 5) 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 * Prolong rate corrected QT (QTc) interval \>= 500 msec. calculated according to institutional guidelines * Left ventricular ejection fraction (LVEF) \< 50% as assessed by echocardiogram or radionuclide angiography * Known moderate to severe chronic obstructive pulmonary disease (COPD), interstitial lung disease, and pulmonary fibrosis * Known hepatic cirrhosis or severe pre-existing hepatic impairment * Major surgery (requiring general anesthesia) within 14 days before the first dose of study drug or a scheduled surgery during study period * Female patients who are both lactating and breastfeeding or have a positive serum pregnancy test during the screening period or a positive urine pregnancy test on day 1 before first dose of study drug * Inability to swallow and retain an oral medication; patients with clinically significant medical condition of malabsorption, inflammatory bowel disease, chronic conditions which manifest with diarrhea, refractory nausea, vomiting or any other condition that will interfere significantly with the absorption of ibrutinib * Active uncontrolled infection or severe infection disease (e.g., severe pneumonia, meningitis, septicemia, or methicillin resistant Staphylococcus aureus infection) * Any condition for which participation in the study is judged by the investigator to be detrimental to the patient with inter-current illness or psychiatric/social situations that would jeopardize compliance with study requirements * Female patients who intend to donate eggs (ova) during the course of this study or 4 months after receiving their last dose of study drug(s) * Male patients who intend to donate sperm during the course of this study or 4 months after receiving their last dose of study drug(s)