Inclusion Criteria:

        Patients eligible for inclusion in this study must meet ALL the following criteria:

          -  Men and woman who are at least 18 years of age on the day of consenting to the study.

          -  Histologically documented PCNSL

          -  Relapsed/refractory PCNSL or newly diagnosed PCNSL patients who are deemed medically
             ineligible by the treating investigator (phase II only) to receive standard first-line
             chemotherapy. All recurrent/refractory patients need to have received at least one
             prior CNS directed therapy. There is no restriction on the number of recurrences.

          -  For recurrent/refractory patients, parenchymal lesions must have unequivocal evidence
             of disease progression on imaging (MRI of the brain or head CT) 21 days of study
             registration. For patients with leptomeningeal disease only, CSF cytology must
             document lymphoma cells and/or imaging findings consistent with CSF disease 21 days of
             study registration (at the discretion of the investigator).

          -  ECOG performance status ≤ 2.

          -  Life expectancy of > 3 months (in the opinion of the investigator).

          -  Adequate bone marrow and organ function shown by:

               -  Absolute neutrophil count (ANC) ≥ 1.5 x 10^9/L

               -  Platelets ≥ 75 x 10^9/L and no platelet transfusion within the past 14 days prior
                  to study registration

               -  Hemoglobin (Hgb) ≥ 8 g/dL and no red blood cell (RBC) transfusion within the past
                  14 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

               -  Lipase ≤ 1.5 x upper limit of normal

          -  Women of childbearing potential (WOCBP) and men must agree to use effective
             contraception when sexually active. This applies for the time period between signing
             of the informed consent form and 30 days (for WOCBP) and 90 days (for men) after the
             last administration of study treatment. A woman is considered of childbearing
             potential, i.e. fertile, following menarche and until becoming post-menopausal unless
             permanently sterile. Permanent sterilization methods include but are not limited to
             hysterectomy, bilateral salpingectomy and bilateral oophorectomy. A postmenopausal
             state is defined as no menses for continuous 12 months without an alternative medical
             cause. A high follicle stimulating hormone (FSH) level in the postmenopausal range may
             be used to confirm a post-menopausal state in women not using hormonal contraception
             or hormonal replacement therapy.

               -  The investigator or a designated associate is requested to advise the patient how
                  to achieve highly effective birth control (failure rate of less than 1%), e.g.
                  intrauterine device (IUD), intrauterine hormone-releasing system (IUS), bilateral
                  tubal occlusion, vasectomized partner and sexual abstinence

               -  The use of condoms by male patients is required unless the female partner is
                  permanently sterile. Female subjects of childbearing potential must have a
                  negative plasma pregnancy test upon study entry

          -  Must be able to tolerate MRI/CT scans

          -  Must be able to tolerate lumbar puncture and/or Ommaya taps

          -  Must have recovered to grade 1 toxicity from prior therapy

          -  Able to submit up to 20 unstained formalin-fixed, paraffin-embedded (FFPE) slides from
             the initial or most recent tissue diagnosis for correlative studies

        NOTE: Prior autologous stem cell transplant as well as prior radiation to the CNS does NOT
        prevent patients from enrollment into the trial.

        Exclusion Criteria:

        Patients eligible for this study must NOT MEET ANY of the following criteria:

          -  Active concurrent malignancy requiring active therapy

          -  Newly diagnosed PCNSL who qualify for standard methotrexate-based chemotherapy

        Excluded medical conditions:

          -  Clinically significant cardiovascular disease such as uncontrolled or symptomatic
             arrhythmias, congestive heart failure (New York Heart Association > Class 2), unstable
             angina, or myocardial infarction within 6 months of screening, or any Class 3 or 4
             cardiac disease as defined by the New York Heart Association Functional Classification

          -  Uncontrolled hypertension despite optimal medical management (per investigator"s
             assessment)

          -  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 is known to have an uncontrolled active systemic infection (>CTCAE grade 2)
             and recent infection requiring intravenous anti-infective treatment that was completed
             ≤14 days before the first dose of study drug

          -  Arterial or venous thrombotic or embolic events such as cerebrovascular accident, deep
             vein thrombosis or pulmonary embolism within 3 months before the start of study
             treatment

          -  Non-healing wound, ulcer or bone fracture

          -  Not recovered to a grade 1 from the toxic effects of prior therapy if clinically
             relevant in the opinion of the investigator (e.g. alopecia)

          -  Known bleeding diathesis (eg, von Willebrand"s disease) or hemophilia

          -  Known history of infection with human immunodeficiency virus (HIV) or history of
             active or chronic infection with hepatitis C virus (HCV) or hepatitis B virus (HBV) as
             determined by serologic tests, or any 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

          -  Unable to swallow capsules or disease significantly affecting gastrointestinal
             function, such as malabsorption syndrome, resection of the stomach or small bowel, or
             complete bowel obstruction

          -  Any life-threatening illness, medical condition including uncontrolled diabetes
             mellitus (DM), uncontrolled hypertension 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

          -  Lactating or pregnant

        Excluded previous Therapies and medications:

          -  Any chemotherapy, external beam radiation therapy, or anticancer antibodies within 21
             days of the first dose of study drug

          -  Prior treatment with a PI3K inhibitor, AKT inhibitor, or mTOR inhibitor (prior
             ibrutinib exposure is allowed)

          -  Any targeted anticancer therapy ≤ 4 weeks or 5 half-lives, whichever is shorter

          -  Use of radio- or toxin-immunoconjugates within 70 days of the first dose of study drug

          -  Concurrent use of warfarin or other vitamin K antagonists (need to be stopped 7 days
             prior to starting on trial drug)

          -  Concurrent use of a strong cytochrome P450 (CYP) 3A4/5 inhibitor and inducers (see
             Appendix 1) (need to be stopped 2 weeks prior to starting on trial drug)

          -  Enzyme-inducing antiepileptic drugs (EIAED) need to be discontinued and switched to a
             nonnon-EIAED 2 weeks prior to starting on trial drug)

          -  Patient requires more than 4 mg of dexamethasone daily or the equivalent

          -  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

          -  Concurrent systemic immunosuppressant therapy (eg, cyclosporine A, tacrolimus, etc.,
             or chronic administration of > 5 mg/day of prednisone) within 28 days of the first
             dose of study drug

          -  Prior allogeneic stem cell transplant