Acalabrutinib and Durvalumab in Primary and Secondary Central Nervous System Lymphoma

Inclusion Criteria: * Histologically documented primary CNS lymphoma with either: * Relapsed or refractory disease with at least 1 prior therapy OR * Ineligible for high dose methotrexate based therapy as determined by the treating physician, including previously untreated patients. Examples of medical conditions that for which a patient could be considered ineligible for high dose methotrexate include renal impairment, liver disease, heart failure or having ascites or effusions. Note: Patients with leptomeningeal disease only must have been previously treated with intrathecal therapy Note: Patients with secondary CNS lymphoma are excluded even if the disease is isolated to the CNS. * Presence of evaluable disease. This includes radiographic evidence of parenchymal disease or leptomeningeal enhancement or thickening, or disease detected in the CSF. Note: Patients with vitreous involvement alone are not eligible. * ECOG performance status of 0, 1, or 2. Patients with ECOG performance status of 3 are permitted if their performance status limitations are due to lymphoma in the opinion of the treating physician. * Adequate bone marrow and organ function shown by: * Absolute neutrophil count (ANC) ≥ 1.0 x 109/L * Platelets ≥ 75 x 10\^9/L and no platelet transfusion within the past 7 days prior to initiation of protocol treatment * Prothrombin time (PT), partial thromboplastin time (PTT), and international normalized ratio (INR) \< 2 times the upper limit of normal (unless attributed to lupus anticoagulant or attributed to anticoagulant such as a direct oral anticoagulant) * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 2.5 times the upper limit of normal * Serum bilirubin ≤ 1.5 times the upper limit of normal * Creatinine clearance \> 30 mL/min calculated by the Cockcroft-Gault formula using actual body weight * Age ≥ 18 years of age * Body weight \>30 kg * Documented negative antibody to HIV * Evidence of post-menopausal status or negative urinary or serum pregnancy test for female pre-menopausal patients. Women will be considered post-menopausal if they have been amenorrheic for 12 months without an alternative medical cause. The following age-specific requirements apply: * Women \<50 years of age would be considered post-menopausal if they have been amenorrheic for 12 months or more following cessation of exogenous hormonal treatments and if they have luteinizing hormone and follicle-stimulating hormone levels in the post-menopausal range for the institution or underwent surgical sterilization (bilateral oophorectomy or hysterectomy). * Women ≥50 years of age would be considered post-menopausal if they have been amenorrheic for 12 months or more following cessation of all exogenous hormonal treatments, had radiation-induced menopause with last menses \>1 year ago, had chemotherapy-induced menopause with last menses \>1 year ago, or underwent surgical sterilization (bilateral oophorectomy, bilateral salpingectomy or hysterectomy). * Have had a hysterectomy and/or bilateral oophorectomy, bilateral salpingectomy, or bilateral tubal ligation/occlusion at least 6 weeks before screening. * Have a congenital or acquired condition that prevents childbearing. * Female subjects of childbearing potential must have a negative pregnancy test no more than 3 days prior to the start of study treatment. * Ability to understand and willingness to sign an IRB approved written informed consent document. Legally authorized representatives may sign and give informed consent on behalf of study participants. Exclusion Criteria: * Diagnosis of secondary CNS lymphoma (even if disease is isolated to CNS). * Vitreous involvement alone. * Concurrent use of other approved or investigational antineoplastic agents (with the exception of corticosteroids) * Participation in another clinical study with an investigational product during the 4 weeks prior to the first day of study treatment. * Prior chemotherapy or targeted small molecule therapy (or other therapy for CNS lymphoma) within 3 weeks prior to the first day of study treatment (or 5 half-lives (whichever is shorter)), or 2 weeks prior to the first day of study treatment for monoclonal antibodies * Recovered to baseline or ≤ grade 1 from prior toxicities of therapy with the exception of alopecia (no recovery required) and neuropathy (recovery to ≤ grade 2 is permitted). * External beam radiation therapy to the CNS within 14 days of the first day of study treatment. * Requires more than 8 mg of dexamethasone daily or the equivalent for control of CNS symptoms at the time of initiation of study therapy. Patients must taper off high dose corticosteroids for the control of CNS symptoms within 14 days after starting on study therapy. * History of intracranial hemorrhage or clinically significant stroke within 6 months prior to first day of study treatment * Inability to swallow oral medications. * History of significant gastrointestinal disease that would limit absorption of oral medications. This could include refractory nausea, vomiting, chronic gastrointestinal disease, bariatric surgery such as gastric bypass, partial or complete bowel obstruction, or previous significant bowel resection that would preclude adequate absorption, distribution, metabolism, or excretion of study treatment. * Active concurrent malignancy requiring active therapy. * Prior therapy with a checkpoint inhibitor, including durvalumab. * Prior therapy with BTK inhibitor. * 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. Use of low molecular weight heparin and novel oral anticoagulants (eg. rivaroxaban, apixaban) is permitted if required. * Concurrent use of a moderate or strong inhibitor or inducer of the P450 isoenzyme CYP3A. Participants must be off P450/CYP3A inhibitors and inducers prior to starting the study drug. Note: Study therapy may be started after 5-half-lives or 7 days (whichever is shorter) have surpassed since last administration of a strong or moderate CYP3A4 inducer/inhibitors. * Use of systemic immunosuppressant therapy, including cyclosporine A, tacrolimus, sirolimus, and other such medications, or chronic administration of \> 10 mg/day of prednisone or the equivalent. This does not refer to patients on corticosteroids for CNS lymphoma symptoms. Participants must be off of immunosuppressant therapy (with the exception of steroids) for at least 14 days prior to the first day of study treatment. The items listed below are exceptions to this criterion: * Intranasal, inhaled, topical steroids, or local steroid injections (e.g., intra articular injection) * Systemic corticosteroids at physiologic doses not to exceed 10 mg/day of prednisone or its equivalent * Steroids as premedication for hypersensitivity reactions (e.g., CT scan premedication) * Receipt of live attenuated vaccine within 30 days prior to the first day of study treatment. Note: Patients, if enrolled, should not receive live vaccine while receiving IP and up to 30 days after the last day of study treatment. * Suspicion of or confirmed progressive multifocal leukoencephalopathy * Active autoimmune disease (including autoimmune hemolytic anemia and immune thrombocytopenia purpura) requiring systemic treatment within the past two years (i.e. with the use of disease modifying agents, corticosteroids, or immunosuppressive drugs). The following are exceptions to this criterion: * Patients with vitiligo or alopecia * Patients with hypothyroidism (e.g., due to Hashimoto syndrome) stable on hormone replacement * Any chronic skin condition that does not require systemic therapy * Patients without active disease in the last 5 years may be included but only after consultation with the study physician * Patients with celiac disease controlled by diet alone * Replacement therapy (e.g. thyroxine, insulin, or physiologic corticosteroids replacement therapy for adrenal or pituitary insufficiency, etc.) * Significant medical diseases or conditions, as assessed by the investigator, that would substantially increase the risk to benefit ratio of participating in the study. This includes, but is not limited to, acute myocardial infarction in the past 6 months, unstable angina, uncontrolled diabetes mellitus, significant active infections,, severely immunocompromised state, and congestive heart failure, New York Heart Association Class III-IV. * Known bleeding diathesis (e.g. von Willebrand's disease), hemophilia, or active bleeding. * Known active infection with hepatitis C virus (HCV) or hepatitis B virus (HBV) as determined by serologic tests and/or PCR. * History of invasive fungal infection, including invasive aspergillosis, or known active tuberculosis. * Major surgery ≤ 28 days prior to starting the trial treatment (or has not recovered from the side effects of such surgery) or plans to have surgery within 2 weeks of the first dose of the study drug. * Prior allogenic stem cell transplant (autologous stem cell transplant is NOT an exclusion).