A Study of ME-401 in Subjects With CLL/SLL, FL, and B-cell Non Hodgkin's Lymphoma

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)