Inclusion Criteria MEI-401 Alone:

          -  Diagnosis of relapsed/refractory CLL and/or relapsed/refractory SLL or FL

          -  No prior therapy with PI3Kd inhibitors

          -  No prior therapy with Bruton tyrosine kinase (BTK) inhibitors unless the subject was
             intolerant of BTK therapy or subject had disease progression

          -  Subjects with CLL/SLL must have prior treatment with BTK inhibitor and must have had
             progression or recurrence while on treatment of within 12 mos from BTK treatment

          -  Subject must have failed at least 1 prior systemic therapy

          -  QT-interval corrected according to Fridericia's formula (QTcF) ≤ 450 milliseconds (ms)

          -  Left ventricular ejection fraction > 50%

          -  For subjects, except those with CLL, must have at least one bi-dimensionally
             measurable nodal lesion >1.5 cm, as defined by Lugano Classification

          -  Willingness to participate in collection of pharmacokinetic samples

          -  A negative serum pregnancy test within 14 days of study Day 0, for females of
             childbearing potential

        Inclusion Criteria ME-401 in Combination with Rituximab

          -  Diagnosis of relapsed/refractory CLL SLL or FL, MZL, DLBCL and high-grade B-cell
             lymphoma. Subjects must meet the following criteria for relapsed or refractory
             disease:

          -  No prior therapy with PI3Kδ inhibitors

          -  No prior therapy with Bruton tyrosine kinase (BTK) inhibitors unless the subject was
             intolerant of BTK therapy or subject had disease progression

          -  Subjects with CLL, SLL, FL, and MZL must have a failure of at least 1 prior systemic
             therapy and be considered by the investigator a candidate for therapy with a
             rituximab-based regimen; subjects with DLBCL and high-grade B-cell lymphoma must have
             a failure of at least 2 prior therapies.

          -  QT-interval corrected according to Fridericia's formula (QTcF) ≤450 milliseconds (ms)

          -  Left ventricular ejection fraction > 50%

          -  For subjects, except those with CLL, must have at least one bi-dimensionally
             measurable nodal lesion >1.5 cm, as defined by Lugano Classification

          -  Willingness to participate in collection of pharmacokinetic samples

          -  A negative serum pregnancy test within 14 days of study Day 0 for females of
             childbearing potential

        Inclusion Criteria ME-401 in Combination with Zanubrutinib

          -  Diagnosis of relapsed/refractory CLL or histologically-confirmed relapsed/refractory
             SLL or FL, MZL, MCL, DLBCL NOS (germinal center B-cell type or activated B-cell type)

          -  No prior therapy with PI3Kδ inhibitors

          -  No prior therapy with BTK inhibitors

          -  Subjects with CLL, SLL, FL, MCL, and MZL must have a failure of at least 1 prior
             systemic therapy, require treatment in the opinion of the investigator, and be
             considered by the investigator a candidate for therapy subjects with DLBCL and
             high-grade B-cell lymphoma must have a failure of at least 2 prior therapies

          -  For subjects with SLL, FL, MZL, MCL, DLBCL: At least one bi dimensionally measurable
             nodal lesion > 1.5 cm in its longest diameter by CT scan or MRI

          -  QT-interval corrected according to Fridericia's formula (QTcF) ≤ 450 milliseconds
             (msec)

          -  Left ventricular ejection fraction > 50% as measured by echocardiogram or multigated
             acquisition (MUGA) scan

          -  Willingness to participate in collection of pharmacokinetic samples

          -  For females of childbearing potential, a negative serum pregnancy test within 14 days
             of study Day 0

        Exclusion Criteria:

          -  Known histological transformation from CLL to an aggressive lymphoma

          -  Uncontrolled autoimmune hemolytic anemia or immune thrombocytopenia

          -  Subjects who have tested positive for hepatitis B surface antigen and/or hepatitis B
             core antibody

          -  Positive for hepatitis C virus antibody (HCV Ab) or human immunodeficiency virus (HIV)
             antibody

          -  Ongoing drug-induced pneumonitis

          -  History of clinically significant cardiovascular abnormalities

          -  History of severe bleeding disorders (ME-401 plus zanubrutinib arm only)

          -  Known central nervous system (CNS) hemorrhage or stroke within 6 months prior to start
             of study drugs (ME-401 plus zanubrutinib arm only)