Negative for hepatitis B, or if infected with hepatitis B, receiving anti-hepatitis B therapy; all participants will be required to be screened for hepatitis B; per Infectious Disease Society of America (IDSA) and Assistance for AIDS Specific Drugs (AASD) guidelines, those participants that show no immunity, defined by the lack of hepatitis B surface antigen antibody, and show evidence of chronic infection (i.e. hepatitis B surface antigen [HBsAg]+, hepatitis B core [HBcore]+, hepatitis B surface antibody [HBsAB]-) will be required to be on anti-hepatitis B therapy during the study in order to be eligible; patients will be permitted to enroll in the study provided normal liver function tests and no evidence of cirrhosis; the exact hepatitis B therapy will be at the discretion of the infection disease specialist or investigator; however all patients who present with acute hepatitis B or show normal transaminases and are hepatitis B virus HBsAg surface protein antigen (HBsAg) positive (+) and immunoglobulin M (IgM)+ for hepatitis core antigen will not be eligible for trial enrollmentXx_NEWLINE_xXPatients diagnosed with hepatitis C who are hepatitis C antibody positive, whether hepatitis C RNA level is measurable or not, must have no evidence of cirrhosis and have liver function testsXx_NEWLINE_xXDocumented cirrhosis or documented acute hepatitis; Note: a positive hepatitis B serology indicative of previous immunization (i.e., hepatitis B surface antibody [HBsAb] positive and hepatitis B core antibody [HBcAb] negative), or a fully resolved acute hepatitis B virus (HBV) infection is not an exclusion criterionXx_NEWLINE_xXFor patients with hepatocellular carcinoma secondary to hepatitis B or C, test results should be indicative of chronic viral hepatitis infection:* Patients with hepatitis B** Antibodies: Hepatitis B surface antigen (HepBsAg) and hepatitis B core antibody (HepBcAb) should be elevated and hepatitis B surface antibody (HepBsAb) and hepatitis Be antibody (HepBeAb) low, indicating chronic infection; if the pattern is different from this, please notify the PI** Viral load: COBAS TaqMan test measuring hepatitis B virus (HBV) DNA is reduced in chronic phase hepatitis B; the baseline value as the patient enters this study will be useful to discriminate between drug, disease progression, or increased viral load as possible attributions for worsening symptoms* Patients with hepatitis C** Antibodies: Anti-hepatitis C virus (HCV) testing-specific tests used will be based on the site�s standard procedure for identifying hepatitis C** Viral load: HCV-RNA should be relatively constant in chronic phase of disease, though the level is typically higher than in the acute phase; the baseline value as the patient enters this study will be useful to discriminate between drug, disease progression, or increased viral load as possible attributions for worsening symptomsXx_NEWLINE_xXA positive hepatitis B serology indicative of previous immunization (i.e., hepatitis B virus surface antibody [HBsAb] positive and hepatitis B virus core antibody [HBcAb] negative), or a fully resolved acute hepatitis B infection is not an exclusion criterionXx_NEWLINE_xXNegative serology (antibody test) for the following infectious diseases:* Human immunodeficiency virus (HIV) type 1 and 2* Human T-cell leukemia virus (HTLV) type 1 and 2 (mandatory in United States [US] but optional in Canada and Europe)* Hepatitis B surface antigen* Hepatitis C antibodyXx_NEWLINE_xXSerologic 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 must have a negative polymerase chain reaction (PCR) prior to enrollment (PCR positive patients will be excluded)Xx_NEWLINE_xXHas 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)Xx_NEWLINE_xXPatients who have a known active hepatitis B or hepatitis C infection are ineligible; patient must have documented evidence of negative tests for the presence of hepatitis B surface antigen and hepatitis C (anti-hepatitis C virus [HCV] antibody OR hepatitis [Hep] C RNA-qualitative); human immunodeficiency virus (HIV)-positive patients are eligible if the following criteria are met:* Stable on their antiretroviral agents* Have CD4 counts above 400* Undetectable viral loads, and* No need for prophylactic medications for an opportunistic infectionsXx_NEWLINE_xXEXCLUSION CRITERIA FOR STRATUM C: Patients who have a known active hepatitis B or hepatitis C infection are ineligible; patient must have documented evidence of negative tests for the presence of hepatitis B surface antigen and hepatitis C (anti-HCV antibody OR Hep C RNA-qualitative); HIV-positive patients are eligible if the following criteria are met:* Stable on their antiretroviral agents* Have CD4 counts above 400* Undetectable viral loads, and* No need for prophylactic medications for an opportunistic infectionsXx_NEWLINE_xXParticipants who have hepatitis C (both reactive anti-hepatitis C virus [HCV] antibody and detectable HCV RNA) and hepatitis B (hepatitis B surface antigen [HBsAg] positive and anti-hepatitis B core [HBc]-total positive), may be enrolled, provided total bilirubin is =< 1.5 x institutional ULN, and AST (SGOT) and ALT (SGPT) must be =< 3 X institutional upper limit of normal, and hepatitis B virus (HBV) deoxyribonucleic acid (DNA) < 100 IU/mL (if hepatitis B positive) within 2 weeks prior to enrollmentXx_NEWLINE_xXPatients cannot have:* Active central nervous system or meningeal involvement by lymphoma; patients with a history of central nervous system (CNS) or meningeal involvement must be in a documented remission by cerebrospinal fluid (CSF) evaluation and contrast-enhanced magnetic resonance imaging (MRI) imaging for at least 91 days prior to registration* Evidence of myelodysplasia or cytogenetic abnormality indicative of myelodysplasia on any bone marrow biopsy prior to initiation of therapy* A known bleeding diathesis* Requirement for warfarin or similar vitamin K antagonists; these drugs are prohibited 28 days prior to the first treatment and throughout the trial* History of stroke or intracranial hemorrhage =< 6 months before treatment* Currently active, clinically significant hepatic impairment (Child-Pugh class B or C according to the Child Pugh classification* History of allergic reactions attributed to compounds of similar chemical or biologic composition to ibrutinib or other agents used in study* 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 must have a negative polymerase chain reaction (PCR) prior to enrollment; (PCR positive patients will be excluded)Xx_NEWLINE_xXKnown serologic status reflecting active hepatitis B or C infection; patients that are hepatitis B core antibody positive, but antigen negative, will need a negative polymerase chain reaction (PCR) prior to enrollment (NOTE: hepatitis B antigen or PCR positive patients will be excluded)Xx_NEWLINE_xXParticipants who are hepatitis C virus antibody positive, or hepatitis B virus surface antigen positive must be free of clinical evidence of cirrhosis as determined by the principal investigator in consultation with the gastroenterology service; timeline: within 3 weeks prior to enrollmentXx_NEWLINE_xXPatients who have hepatitis C (both reactive anti-hepatitis C virus [HCV] antibody and detectable HCV RNA) and hepatitis B (hepatitis B surface antigen [HBsAg] positive and anti-hepatitis B core [HBc]-total positive), may be enrolled, provided their total bilirubin: =< 1.5 x institutional upper limit of normal (ULN) AST (SGOT)/ALT (SGPT): =< 2.5 x institutional upper limit of normalXx_NEWLINE_xXPatients must not have a known positive test for hepatitis B virus surface antigen (HBV sAg) or hepatitis C virus ribonucleic acid (HCV antibody) indicating acute or chronic infection; patients with a positive hepatitis C antibody with a negative viral load are allowedXx_NEWLINE_xXDocumented human immunodeficiency virus (HIV), active bacterial infections, active or chronic hepatitis B, hepatitis C* Positive hepatitis B serology indicative of previous immunization (i.e., hepatitis B surface antigen [HBsAb] positive and hepatitis B core antibody [HBcAb] negative) or a fully resolved acute hepatitis B infection is not an exclusion criterion* Positive hepatitis C serology is an exclusion criterionNOTE: HIV-positive patients are excluded from the studyXx_NEWLINE_xXKnown clinically significant liver disease, including active viral, alcoholic, or other hepatitis; cirrhosis; fatty liver; and inherited liver disease.* Patients with past or resolved hepatitis B infection (defined as having a negative hepatitis B surface antigen [HBsAg] test and a positive anti-HBc [antibody to hepatitis B core antigen] antibody test) are eligible* Patients positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction (PCR) is negative for HCV ribonucleic acid (RNA)Xx_NEWLINE_xXKnown clinically significant liver disease, including active viral, alcoholic, or other hepatitis; cirrhosis; fatty liver; and inherited liver disease* Patients with past or resolved hepatitis B infection (defined as having a negative hepatitis B surface antigen [HBsAg] test and a positive anti-HBc [antibody to hepatitis B core antigen] antibody test) are eligible* Patients positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction (PCR) is negative for HCV ribonucleic acid (RNA)Xx_NEWLINE_xXPatients must not have active hepatitis B (chronic or acute) or active hepatitis C infection* Patients with past or resolved hepatitis B infection (defined as having a negative hepatitis B surface antigen [HBsAg] test and a positive anti-HBc [antibody to hepatitis B core antigen] antibody test) are eligible* Patients positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction (PCR) is negative for HCV RNAXx_NEWLINE_xXKnown clinically significant liver disease, including active viral, alcoholic, or other hepatitis; cirrhosis; fatty liver; and inherited liver disease* Patients with past or resolved hepatitis B infection (defined as having a negative hepatitis B surface antigen [HBsAg] test and a positive anti-HBc [antibody to hepatitis B core antigen] antibody test) are eligible* Patients positive for hepatitis C virus (HCV) antibody are eligible only if PCR is negative for HCV RNAXx_NEWLINE_xXPatients with known clinically significant liver disease (have previously tested positive), including active viral, alcoholic, or other hepatitis; cirrhosis; fatty liver; and inherited liver disease* Patients with past or resolved hepatitis B infection (defined as having a negative hepatitis B surface antigen [HBsAg] test and a positive anti-HBc [antibody to hepatitis B core antigen] antibody test) are eligible* Patients positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction (PCR) is negative for HCV ribonucleic acid (RNA)Xx_NEWLINE_xXHistory of any chronic hepatitis including alcoholic, non-alcoholic steatohepatitis (NASH), drug related, autoimmune, chronic viral positive tests for hepatitis B virus surface antigen (HBsAg), hepatitis B core antibody (anti-HBc) in the absence of hepatitis B surface antibody (anti-HBs), or a positive hepatitis C (HCV) viral load; these patients are excludedXx_NEWLINE_xXKnown clinically significant liver disease, including active viral, alcoholic, or other hepatitis; cirrhosis; fatty liver; and inherited liver disease* Patients with past or resolved hepatitis B infection (defined as having a negative hepatitis B surface antigen [HBsAg] test and a positive anti-HBc [antibody to hepatitis B core antigen] antibody test) are eligible* Patients positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction (PCR) is negative for HCV ribonucleic acid (RNA)Xx_NEWLINE_xXActive infection including hepatitis B (known positive hepatitis B virus [HBV] surface antigen [HBsAg]) result or, hepatitis C; patients with a past or resolved HBV infection (defined as the presence of hepatitis B core antibody [anti-HBc] and absence of HBsAg) are eligible; patients positive for hepatitis C (HCV) antibody are eligible only if polymerase chain reaction is negative for HCV ribonucleic acid (RNA); negative serologies documented over the past year are sufficient evidence of thisXx_NEWLINE_xXKnown clinically significant liver disease, including active viral, alcoholic, or other hepatitis; cirrhosis; fatty liver; and inherited liver disease* Patients with past or resolved hepatitis B infection (defined as having a negative hepatitis B surface antigen [HBsAg] test and a positive anti-HBc [antibody to hepatitis B core antigen] antibody test) are eligible* Patients positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction (PCR) is negative for HCV ribonucleic acid (RNA)Xx_NEWLINE_xXPatients with a known positive test for hepatitis B virus surface antigen (HBV sAg) or hepatitis C virus ribonucleic acid (HCV antibody) indicating acute or chronic infection might be enrolled if the viral load by polymerase chain reaction (PCR) is undetectable with/without active treatmentXx_NEWLINE_xXPatients must not have known human immunodeficiency virus (HIV), or a known positive test for hepatitis B virus surface antigen (HBV sAg), or hepatitis C virus ribonucleic acid (HCV antibody) indicating current acute or chronic infection; patients with a positive hepatitis C antibody with a negative viral load are allowedXx_NEWLINE_xXKnown clinically significant liver disease, including active viral, alcoholic, or other hepatitis; cirrhosis; fatty liver; and inherited liver disease* Patients with past or resolved hepatitis B infection (defined as having a negative hepatitis B surface antigen [HBsAg] test and a positive anti-HBc [antibody to hepatitis B core antigen] antibody test) are eligible* Patients positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction (PCR) is negative for HCV ribonucleic acid (RNA)Xx_NEWLINE_xX