UK Center for Clinical and Translational Science

(Part A) 1. Written informed consent by the patient prior to screening 2. Patients aged ≥ 18 years on the day of consenting to the study 3. Pathologic diagnosis of PCNSL 4. Relapse or refractory PCNSL with at least one prior high dose methotrexate (HD-MTX) based therapy for PCNSL 5. Measurable brain lesion with a minimum diameter > 1.0 cm in gadolinium enhanced magnetic resonance imaging (MRI) performed within 14 days before starting tirabrutinib treatment 6. Eastern Cooperative Oncology Group performance score (ECOG PS) of 0, 1 or 2 7. Life expectancy of at least 3 months 8. Adequate bone marrow, renal, and hepatic function Inclusion Criteria (Part B) 1. Written informed consent by the patient prior to screening 2. Patients aged ≥ 18 years on the day of consenting to the study 3. Pathologic diagnosis of PCNSL within the past 3 months 4. No prior anti-tumor treatments for PCNSL 5. Patients who, in the opinion of the Investigator, are suitable to receive treatment with a high dose methotrexate containing regimen 6. Measurable brain lesion with a minimum diameter > 1.0 cm in gadolinium enhanced MRI performed within 14 days before starting study treatment 7. ECOG PS of 0, 1 or 2 8. Life expectancy of at least 6 months 9. Adequate bone marrow, renal, and hepatic function

(Part A) 1. Intraocular PCNSL with no brain lesion 2. Patient who is intolerant of contrast enhanced MRI due to allergic reactions to contrast agents 3. Patient with non-B cell PCNSL 4. Patient with systemic presence of lymphoma 5. Prior chemotherapy within 21 days, nitrosourea within 42 days, an antibody drug with anticancer activity (e.g., rituximab) within 28 days, prior radiotherapy within 14 days, prior major invasive surgery within 28 days, or allogeneic stem cell transplant within 6 months before starting tirabrutinib treatment 6. Prior BTK inhibitor treatment 7. Prior investigational drugs (including treatment in clinical research, unapproved combination products, and new dosage forms) within 28 days or 5 half-lives, whichever is shorter, before starting tirabrutinib treatment 8. Concomitant systemic corticosteroid on an ongoing basis within 14 days before starting tirabrutinib treatment, with the exception of the following: - Equivalent of up to 10 mg/day of prednisone for a disease other than PCNSL - Equivalent of up to 50 mg/day of prednisone (equal to 8 mg/day of dexamethasone) for patients with lesions of the brain or spinal cord or both 9. Patient who has received a CYP3A4 inducer or P-gp inducer within 14 days before starting tirabrutinib treatment 10. Concomitant warfarin, any other warfarin derivative anticoagulant, vitamin K antagonists, novel oral anticoagulants, or antiplatelet therapy on an ongoing basis within 7 days before starting tirabrutinib treatment 11. Active malignancy, other than PCNSL requiring systemic therapy 12. Poorly controlled comorbidity, severe heart, severe lung disease, clinically significant liver diseases that could affect protocol compliance or safety or efficacy assessments 13. Patient with bleeding diathesis 14. Patients with a history of moderate or severe hepatic impairment 15. QTcF > 480 milliseconds or requirement for ongoing treatment with concomitant medications that prolong the QT interval 16. Active infection, including a HIV, cytomegalovirus infection or SARS-CoV-2, or has had, within 28 days before starting tirabrutinib treatment, an infection (other than nail trichophytosis) that requires hospitalization or an intravenous antibiotic 17. Prior history of hypersensitivity or anaphylaxis to tirabrutinib 18. Prior history of Stevens Johnson Syndrome or Toxic Epidermal Necrolysis 19. Medical history of organ allografts 20. Tests positive for HIV-1 antibody and HIV-2 antibody, human T-lymphotropic virus 1 antibody, hepatitis B (HB) antigen, or hepatitis C virus (HCV) antibody. Tests positive for HBs antibody or hepatitis B virus core protein antibody and has a result of at least detectable in a hepatitis B virus deoxyribonucleic acid assay despite testing negative for HBs antigen. 21. Patient is unable to swallow tablets; has malabsorption, malabsorption syndrome, or a comorbidity that affects gastric function; has undergone complete resection of the stomach or small intestine; has ulcerative colitis or symptomatic inflammatory bowel disease; or has partial or complete intestinal obstruction. 22. Women who are pregnant or lactating 23. Patient is found incapable of giving consent due to dementia or another such condition 24. Patient is found to be otherwise ineligible for the study by the Investigator or sub-Investigator. Exclusion Criteria (Part B) 1. Intraocular PCNSL with no brain lesion 2. Patients for whom the selected backbone regimen medications (i.e, methotrexate/temozolomide/rituximab for MTR and rituximab/methotrexate/procarbazine/vincristine for R-MPV) are contraindicated 3. Patients with a history of intolerable toxicity, hypersensitivity, anaphylaxis to the selected backbone regimen medications 4. Patient who is intolerant of contrast enhanced MRI due to allergic reactions to contrast agents 5. Patient with non-B cell PCNSL 6. Patient with systemic presence of lymphoma 7. Prior chemotherapy within 21 days, nitrosourea within 42 days, an antibody drug with anticancer activity (e.g., rituximab) within 28 days, prior radiotherapy within 14 days, prior major invasive surgery within 28 days, or allogeneic stem cell transplant within 6 months before starting tirabrutinib treatment 8. Prior BTK inhibitor treatment 9. Prior investigational drugs (including treatment in clinical research, unapproved combination products, and new dosage forms) within 28 days or 5 half-lives, whichever is shorter, before starting tirabrutinib treatment 10. Concomitant systemic corticosteroid on an ongoing basis within 14 days before starting tirabrutinib treatment, with the exception of the following: - Equivalent of up to 10 mg/day of prednisone for a disease other than PCNSL - Equivalent of up to 50 mg/day of prednisone (equal to 8 mg/day of dexamethasone) for patients with lesions of the brain or spinal cord or both 11. Patient who has received a CYP3A4 inducer or P-gp inducer within 14 days before starting tirabrutinib treatment 12. Concomitant warfarin, any other warfarin derivative anticoagulant, vitamin K antagonists, novel oral anticoagulants, or antiplatelet therapy on an ongoing basis within 7 days before starting tirabrutinib treatment 13. Active malignancy, other than PCNSL requiring systemic therapy 14. Poorly controlled comorbidity, severe heart, severe lung disease, clinically significant liver diseases that could affect protocol compliance or safety or efficacy assessments 15. Patient with bleeding diathesis 16. Patients with a history of moderate or severe hepatic impairment 17. QTcF > 480 milliseconds or requirement for ongoing treatment with concomitant medications that prolong the QT interval 18. Active infection, including a HIV, cytomegalovirus infection or SARS-CoV-2, or has had, within 28 days before starting tirabrutinib treatment, an infection (other than nail trichophytosis) that requires hospitalization or an intravenous antibiotic 19. Prior history of hypersensitivity or anaphylaxis to tirabrutinib 20. Prior history of Stevens Johnson Syndrome or Toxic Epidermal Necrolysis 21. Medical history of organ allografts 22. Tests positive for HIV-1 antibody and HIV-2 antibody, human T-lymphotropic virus 1 antibody, HBs antigen, or HCV antibody. Tests positive for HBs antibody or hepatitis B virus core protein antibody and has a result of at least detectable in a hepatitis B virus deoxyribonucleic acid assay despite testing negative for HBs antigen. 23. Patient is unable to swallow tablets; has malabsorption, malabsorption syndrome, or a comorbidity that affects gastric function; has undergone complete resection of the stomach or small intestine; has ulcerative colitis or symptomatic inflammatory bowel disease; or has partial or complete intestinal obstruction. 24. Women who are pregnant or lactating 25. Patient is found incapable of giving consent due to dementia or another such condition 26. Patient is found to be otherwise ineligible for the study by the Investigator or sub-Investigator.