Pembrolizumab and Ibrutinib in Treating Patients With Relapsed or Refractory Non-Hodgkin Lymphoma

Inclusion Criteria: * Histologically confirmed B-cell NHL with any of the following subtypes: diffuse large B-cell lymphoma (DLBCL), mantle cell lymphoma (MCL), follicular lymphoma (FL), marginal zone lymphoma (MZL) and lymphoplasmacytic lymphoma/Waldenstrom's macroglobulinemia (LL/WM), Burkitt's lymphoma (BL); patients with histological transformation to DLBCL from indolent lymphoma, primary mediastinal lymphoma and grey zone lymphoma are eligible (Part 1) * Patients must have received at least one prior therapy; prior autologous stem cell transplant is permitted; patients with DLBCL who have not had prior high-dose therapy (HDT)/autologous stem cell transplant (ASCT) must be ineligible for transplant; prior ibrutinib is not permitted if patients have progressed on therapy (Part 1) * Patients with Waldenstrom's macroglobulinemia (WM) must meet the indications for treatment per the International Workshop on Waldenstrom's Macroglobulinemia (IWWM) (Part 1) * Histologically confirmed B-cell NHL (Part 2): * Group 1: with only de novo DLBCL, * Group 2: with only FL of grade 1, 2 or 3a * Group 3: with only MCL with t(11;14) or overexpression of cyclin D1 * Group 4: all other NHL including MZL, LL, WM, BL, primary mediastinal B cell lymphoma (PMBCL), gray zone lymphoma (GZL) and patients with histological transformation to DLBCL from indolent lymphoma are eligible * Patients must have received at least one prior therapy; prior autologous stem cell transplant is permitted; patients with DLBCL who have not had prior HDT/ASCT must be ineligible for transplant; prior ibrutinib is not permitted if patients have progressed on therapy (Part 2) * Patients with Waldenstrom's macroglobulinemia (WM) must meet the indications for treatment per the International Workshop on Waldenstrom's Macroglobulinemia (IWWM) (Part 2) * Be willing and able to provide written informed consent/assent for the trial * Have evaluable disease * Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 * Absolute neutrophil count (ANC) \>= 1,000/mcL * Platelets \>= 50,000/mcL in the absence of transfusion support within 7 days of determining eligibility * Hemoglobin \>= 8 g/dL * Serum creatinine =\< 1.5 X upper limit of normal (ULN) OR measured or calculated creatinine clearance (glomerular filtration rate \[GFR\] can also be used in place of creatinine or creatinine clearance \[CrCl\]) OR \>= 60 mL/min for subject with creatinine levels \> 1.5 X institutional ULN * Serum total bilirubin =\< 1.5 X ULN OR direct bilirubin =\< ULN for subjects with total bilirubin levels \> 1.5 ULN * Aspartate aminotransferases (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X ULN OR =\< 5 X ULN for subjects with liver metastases * Albumin \>= 2.5 mg/dL * International normalized ratio (INR) or prothrombin time (PT) =\< 1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or partial thromboplastin time (PTT) is within therapeutic * Activated partial thromboplastin time (aPTT) =\< 1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants * Female subject of childbearing potential should have a negative urine or serum pregnancy within 72 hours prior to receiving the first dose of study medication; if the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Female subjects of childbearing potential should be willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 120 days after the last dose of study medication; subjects of childbearing potential are those who have not been surgically sterilized or have not been free from menses for \> 1 year * Male subjects should agree to use an adequate method of contraception starting with the first dose of study therapy through 120 days after the last dose of study therapy Exclusion Criteria: * Is currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy or used an investigational device within 4 weeks of the first dose of treatment * Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment; subjects may use topical or inhaled corticosteroids or low-dose steroids (=\< 10 mg of prednisone or equivalent per day) as therapy for comorbid conditions; during study participation, subjects may receive systemic or enteric corticosteroids as needed for treatment-emergent comorbid conditions * Has a known history of active TB (Bacillus tuberculosis) * Hypersensitivity to pembrolizumab or ibrutinib or any of their excipients * Has had a prior anti-cancer monoclonal antibody (mAb) within 4 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to agents administered more than 4 weeks earlier * Has had prior chemotherapy or radiation therapy within 2 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to a previously administered agent * Note: subjects with =\< grade 2 neuropathy are an exception to this criterion and may qualify for the study * Note: if subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy; patients must be 4 weeks out from major procedures and 2 weeks out from minor procedures * Has a known additional malignancy that is progressing or requires active treatment; exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer * Has known active central nervous system (CNS) lymphoma * Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs); replacement therapy (eg., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment * Has known history of, or any evidence of active, non-infectious pneumonitis * Has evidence of immune- mediated hepatitis, nephritis, or thyroiditis * Has evidence of interstitial lung disease * Has evidence of colitis * Has undergone prior allogeneic hematopoietic stem cell transplantation within the last 5 years * Requires treatment with a strong CYP3A4 inhibitor/inducer * Known bleeding disorders * Requires therapeutic anticoagulation with warfarin or other vitamin K antagonists * History of stroke or intracranial hemorrhage within 6 months of the first dose of study drug * Has an active infection requiring intravenous systemic therapy * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial * Is unable to swallow capsules or malabsorption syndrome, disease or condition significantly affecting gastrointestinal function * Clinically significant cardiovascular disease with uncontrolled arrhythmia, New York Association class 3 or 4 congestive heart failure, history of myocardial infarction within 6 months, or prolonged corrected QT (QTc) \> 500 msec * Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment * Has received prior therapy with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent * Has progressed on prior therapy with ibrutinib or other BTK inhibitors * Has a known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies) * Has known active hepatitis B (e.g., hepatitis B surface antigen \[HBsAg\] reactive) or hepatitis C (e.g., hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] \[qualitative\] is detected) * Has received a live vaccine within 30 days of planned start of study therapy * Note: seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist) are live attenuated vaccines, and are not allowed