Ibrutinib and Combination Chemotherapy in Treating Patients With Relapsed or Refractory Diffuse Large B-cell Lymphoma

Inclusion Criteria:

* Autologous transplant eligible patients must have histologically or cytologically confirmed cluster of differentiation (CD)20 positive relapsed or refractory DLBCL by biopsy within 45 days prior to subject enrollment and must have been previously treated with an anthracycline and rituximab-containing regimen
* Baseline fludeoxyglucose F 18 (FDG)-positron emission tomography (PET) scans must demonstrate positive lesions compatible with computed tomography (CT) defined anatomical tumor sites

  * CT scan showing at least:

    * 2 or more clearly demarcated lesions/nodes with a long axis \> 1.5 cm and short axis \>= 1.0 cm OR
    * 1 clearly demarcated lesion/node with a long axis \> 2.0 cm and short axis \>= 1.0 cm
* Patient must have been previously treated for B cell non-Hodgkin lymphoma with any of the allowable below:

  * First-line treatment with rituximab and an anthracycline-based chemotherapy
  * Monotherapy rituximab, dosed prior to first-line rituximab combined with anthracycline containing chemotherapy, or as maintenance therapy
  * Radiotherapy as part of the first-line treatment plan including anthracycline and rituximab
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%)
* Life expectancy of greater than 6 weeks
* Absolute neutrophil count \>= 1,000/mcL (unless due to lymphoma involvement of the bone marrow)
* Platelets \>= 75,000/mcL (unless due to lymphoma involvement of the bone marrow)
* Total bilirubin \< 1.5 x within normal institutional limits (unless due to lymphoma involvement of liver or a known history of Gilbert's disease)
* Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 × institutional upper limit of normal (unless due to lymphoma involvement of liver)
* Creatinine within normal institutional limits OR creatinine clearance \>= 40 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal (unless due to lymphoma)
* 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 90 days after the last dose of study drug; 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
* Ibrutinib must be discontinued 7 days before (when possible) until 7 days after major surgery, and 3 days before (when possible) until 3 days after minor surgery; thus, patients to be enrolled on an ibrutinib trial must have completed major surgery within 4 weeks before initiating treatment, and/or must have completed minor surgery \> 3 days before initiating treatment
* Ability to understand and the willingness to sign a written informed consent document
* Must be able to swallow whole capsules

Exclusion Criteria:

* Patients who have had chemotherapy or radiotherapy =\< 21 days (=\< 6 weeks for monoclonal antibodies) prior to first administration of study treatment or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier
* Patients who are receiving any other investigational agents
* Patients with known brain metastases should be excluded from this clinical trial
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to ibrutinib or R-ICE
* Requires treatment with a strong cytochrome P450 (CYP) 3A inhibitor; strong inhibitors or inducers of CYP3A4/5 should be avoided and moderate inhibitors or inducers should be used with caution; it is important to regularly consult a frequently-updated list; medical reference texts such as the Physicians' Desk Reference may also provide this information; 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
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements; recent infections requiring systemic treatment need to have completed therapy \> 14 days before the first dose of study drug
* Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with ibrutinib R-ICE
* Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are eligible, unless the patient's CD4 count is below the institutional lower limit of normal, or the patient is taking prohibited CYP3A4/5 strong inhibitors or inducers
* Patients may not have received any anti-cancer therapy for their primary relapsed (rel)/refractory (ref) DLBCL with the exception of palliative radiation therapy (RT)
* Uncontrolled autoimmune hemolytic anemia or idiopathic thrombocytopenic purpura (ITP) resulting in (or as evidenced by) declining platelet or hemoglobin (Hgb) levels within the 4 weeks prior to first dose of study drug
* Presence of transfusion-dependent thrombocytopenia
* Prior exposure to bruton tyrosine kinase (BTK) inhibitor
* History of prior malignancy, with the exception of the following:

  * Malignancy treated with curative intent and with no evidence of active disease present for more than 3 years prior to screening and felt to be at low risk for recurrence by treating physician
  * Adequately treated non-melanomatous skin cancer or lentigo maligna melanoma without current evidence of disease
  * Adequately treated cervical carcinoma in situ without current evidence of disease
* Currently active clinically significant cardiovascular disease such as uncontrolled arrhythmia, congestive heart failure, or class 3 or 4 congestive heart failure as defined by the New York Heart Association Functional Classification, or history of myocardial infarction, unstable angina, or acute coronary syndrome within 6 months prior to first dose with study drug
* Unable to swallow capsules, or disease significantly affecting gastrointestinal function or resection of the stomach or small bowel, or symptomatic-inflammatory bowel disease or ulcerative colitis, or partial or complete bowel obstruction
* Serologic status reflecting active hepatitis B or C infection; patients that are positive for hepatitis B core antibody, hepatitis B surface antigen (HBsAg), or hepatitis C antibody will need a negative polymerase chain reaction (PCR) prior to enrollment (PCR positive patients will be excluded); hepatitis C antibody positive patients are eligible if PCR is negative
* History of stroke or intracranial hemorrhage within 6 months prior to enrollment
* Current life-threatening illness, medical condition, or organ system dysfunction which, in the Investigator's opinion, could compromise the patient's safety, or put the study at risk
* Received anticoagulation therapy with Coumadin or equivalent vitamin K antagonists within the last 28 days
* Vaccinated with live, attenuated vaccines with 4 weeks of first does of study drug
* Unresolved toxicities from prior anti-cancer therapy, defined as having not resolved to Common Terminology Criteria for Adverse Event (CTCAE, version 4), grade =\< 1, or to the levels dictated in the inclusion/exclusion criteria with the exception of alopecia
* Known bleeding disorders (e.g., von Willebrand's disease) or hemophilia
* Unwilling or unable to participate in all required study evaluations and procedures
* Currently active, clinically significant hepatic impairment \>= moderate hepatic impairment according to the National Cancer Institute (NCI)/Child Pugh classification