Bruton's Tyrosine Kinase (BTK) Inhibitor, Ibrutinib, in Patients With Newly Diagnosed or Refractory/Recurrent Primary Central Nervous System Lymphoma (PCNSL) and Refractory/Recurrent Secondary Central Nervous System Lymphoma (SCNSL)

The population consists of adult patients with newly diagnosed or relapsed or refractory primary central nervous system lymphoma (PCNSL) or relapsed or refractory secondary central nervous system lymphoma (SCNSL) Patients eligible for inclusion in this study have to meet all the following criteria: Inclusion Criteria: * Participants must be able to understand and be willing to sign a written informed consent document * Men and woman who are at least 18 years of age on the day of consenting to the study * Histologically or cystologically documented PCNSL or histologically documented systemic diffuse large B-cell lymphoma (DLBCL) * Patients must have relapsed/refractory PCNSL or relapsed/refractory SCNSL (Arm A, B, C) or newly diagnosed PCNSL (Arm D) * All patients need to have received at least one prior CNS directed therapy. There is no restriction on the number of recurrences (Arm A, B , C only) * Patients with parenchymal lesions must have unequivocal evidence of disease progression on imaging (MRI of the brain or head CT) 21 days prior to study registration. For patients with leptomeningeal disease only, CSF cytology must document lymphoma cells and/or imaging findings consistent with CSF disease 21 days prior to study registration (at the discretion of the investigator) (Arm A, B , C only). * Participants must have an ECOG performance status of 0, 1, or 2 * Within the past 21 days prior to study registration (for Arm D: prior to treatment initiation) participants must have adequate bone marrow and organ function shown by: * Absolute neutrophil count (ANC) ≥ 0.75 x 109/L * Platelets ≥ 75 x 109/L and no platelet transfusion within the past 21 days prior to study registration * Hemoglobin (Hgb) ≥ 8 g/dL and no red blood cell (RBC) transfusion within the past 21 days prior to study registration * International Normalized Ratio (INR) ≤ 1.5 and PTT (aPTT) ≤ 1.5 times the upper limit of normal * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 3 times the upper limit of normal * Serum bilirubin ≤ 1.5 times the upper limit of normal; or total bilirubin ≤ 3 times the upper limit of normal with direct bilirubin within the normal range in patients with well documented Gilbert Syndrome * Serum creatinine ≤ 2 times the upper limit of normal * Arm C: calculated creatinine clearance(CrCl) \> 50ml/min using the Cockcroft-Gault equation (Men: CrCl (min/ml) = (140-age) X (actual weight in kg) / 72 X serum creatinine (mg/dL); Women: CrCl (ml/min) = (140-age) X (actual weight in kg) X 0.85 / 72 X serum creatinine (mg/dL)) * Woman of reproductive potential must agree to use highly effective methods of birth control during the period of therapy and for 30 days after the last dose of the study drug. Men who are sexually active must agree to use highly effective contraception during the period of therapy and for 3 months after the last dose * Female subjects of childbearing potential must have a negative plasma pregnancy test upon study entry. See section on Pregnancy and Reproduction * Patients must be able to tolerate MRI/CT scans * Patients must be able to tolerate lumbar puncture and/or Ommaya taps * Participants must have recovered to grade 1 toxicity from prior therapy (Arm A, B , C only) * Participates must be able to submit 20 unstained formalin-fixed, paraffin-embedded (FFPE) slides from the initial tissue diagnosis prior to study registration for confirmation of diagnosis and correlative studies Arm C1 and C2: SCNSL patients do not require one prior CNS directed treatment. Newly diagnosed SCNSL patients are eligible as long as their systemic disease has been treated and does not require any active treatment. Arm D: PCNSL patients without one prior CNS directed treatment. Exclusion Criteria: * Patients with SCNSL actively receiving treatment for extra-CNS disease are excluded * Patient is concurrently using other approved or investigational antineoplastic agents. Investigational supportive agents are permitted. * Patient has received chemotherapy, monoclonal antibodies or targeted anticancer therapy ≤ 4 weeks or 5 half-lives, whichever is shorter, or 6 weeks for nitrosurea, or mitomycin-C prior to starting the study drug, or the patient has not recovered from the side effects of such therapy Patient has received external beam radiation therapy to the CNSwithin 21 days of the first dose of the study drug * Patient requires more than 8 mg of dexamethasone daily or the equivalent therapy (Arm A, B , C only) * Patient has an active concurrent malignancy requiring active therapy * The patient has been treated with radio- or toxin-immunoconjugates within 70 days of the first dose of the study drug * Patient has previously taken is allergic to components of the study drug. For Arms A and B only: Patient has previously taken ibrutinib. * Patient is using warfarin or any other Coumadin-derivative anticoagulant or vitamin K antagonists. Patients must be off warfarin-derivative anticoagulants for at least seven days prior to starting the study drug. Low molecular weight heparin is allowed. Patients with congenital bleeding diathesis are excluded * Patient is taking a drug known to be a moderate and strong inhibitor or inducers of the P450 isoenzyme CYP3A. Participants must be off P450/CYP3A inhibitors and inducers for at least two weeks prior to starting the study drug * Patient is using systemic immunosuppressant therapy, including cyclosporine A, tacrolimus, sirolimus, and other such medications, or chronic administration of \> 5 mg/day or prednisone or the equivalent. Participants must be off of immunosuppressant therapy for at least 28 days prior to the first dose of the study drug * Patient has significant abnormalities on screening electrocardiogram (EKG) and active and significant cardiovascular disease such as uncontrolled or symptomatic arrhythmias, congestive heart failure, hypertension, valvular disease, pericarditis, or myocardial infarction within 6 months of screening * Patient has a known bleeding diathesis (e.g. von Willebrand's disease) or hemophilia * Patient is known to have human immunodeficiency virus (HIV) infection * Patient is known to have a history of active or chronic infection with hepatitis C virus (HCV) or hepatitis B virus (HBV) as determined by serologic tests * Patient is known to have an uncontrolled active systemic infection * Patient underwent major systemic surgery ≤ 2 weeks prior to starting the trial treatment or who has not recovered from the side effects of such surgery, or who plan to have surgery within 2 weeks of the first dose of the study drug therapy (Arm A, B , C only). * Patient is unable to swallow capsules or has a disease or condition significantly affecting gastrointestinal function, such as malabsorption syndrome, resection of the stomach or small bowel, or complete bowel obstruction * Patient has poorly controlled diabetes mellitus with a glycosylated hemoglobin \>8% or poorly controlled steroid-induced diabetes mellitus with a glycosylated hemoglobin of \>8% * Patient has a life-threatening illness, medical condition, or organ system dysfunction that, in the opinion of the investigator, could compromise the subject's safety or put the study outcomes at undue risk * Women who are pregnant or nursing (lactating), where pregnancy is defined as a state of a female after conception until the termination of gestation, confirmed by a positive serum hCG laboratory test of \> 5 mIU/mL (See section on Pregnancy and Reproduction) * Patient has undergone prior allogenic stem cell transplant (autologous stem cell transplant is NOT an exclusion) * The patient is unwell or unable to participate in all required study evaluations and procedures * Patient is unable to understand the purpose and risks of the study and to provide a signed and dated informed consent form (ICF) and authorization to use protected health information (PHI) in accordance with national and local subject privacy regulations. A legal representative can consent on behalf of a patient who is able to understand the purpose and risk of the study but not able to provide a signature on the ICF and authorization to use PHI due to neurologic deficits (e.g. motor or language deficits) (Arm A, B , C only) Arm C and D: Patients with a methotrexate allergies are excluded. Arm D: Patients with pre-existing peripheral motor or sensory neuropathy ≥ grade 3 (CTCAE 5.0)