Inclusion Criteria:  Dose-Escalation Stage (Cohort A) and Cohort-Expansion Stage (B-E): The subject has received standard life-prolonging therapies or are not qualified to receive such therapies. Dose-Escalation Stage (Cohort A): Subjects with histologically documented diagnosis of B-cell or T-cell Non-Hodgkin's Lymphoma as defined by the World Health Organization (WHO) classification. Note: Refer to exclusion criteria for lymphoma subtypes which are excluded from study participation. Cohort-Expansion Stage Cohort B (ABC-DLBCL subtype): Subjects with histologically documented activated B-cell diffuse large B-cell lymphoma (ABC-DLBCL) subtype. Note: De novo or transformed diffuse large B-cell lymphoma (DLBCL) from previously diagnosed indolent lymphoma (eg, follicular lymphoma) is allowed. Cohort-Expansion Stage Cohort C (MCL): Subjects with histologically documented MCL with monoclonal B-cells that show a chromosome translocation t(11;14)(q13;q32) and/or overexpression of cyclin D1. Cohort-Expansion Stage Cohort D (CLL/SLL): Subjects with histologically documented CLL/SLL per the International Workshop on Chronic Lymphocytic Leukemia (iwCLL) guidelines. Cohort-Expansion Stage Cohort E, Biomarker Cohort (ABC-DLBCL, MCL, and SLL): Subjects with ABC-DLBCL, MCL, and SLL that fulfill the subject disease characteristics criteria as described for Cohorts B, C, or D. Cohort-Expansion Stage: Subjects with ABC-DLBCL, MCL, and SLL must have measurable disease by revised criteria for response assessment of lymphoma. Cohort-Expansion Stages: Must have archival tumor tissue available, which was collected up to 2 years prior to consent for this study. If archival tumor tissue is not available, a fresh tumor biopsy may be obtained (if safe to acquire) up to 60 days prior to first dose. Biomarker Cohort: Subjects must provide a fresh tumor biopsy up to 60 days prior to first dose, at week 2, day 1 (W2D1) after initiation of XL114, and at disease progression. Note: The tumor tissue requirement in the Expansion and Biomarker cohorts doesn't apply for subjects with CLL. Recovery to baseline or ≤ Grade 1 severity (Common Terminology Criteria for Adverse Events version 5 [CTCAE v5]) from AEs, unless AEs are clinically nonsignificant or stable. Left ventricular ejection fraction (LVEF) > 50% as determined by echocardiogram (ECHO) or multigated acquisition (MUGA) scan per local standard. Age 18 years or older on the day of consent. Eastern Cooperative Oncology Group Performance Status (ECOG PS) of 0-1 Adequate organ and marrow function Sexually active fertile subjects and their partners must agree to highly effective methods of contraception. Female subjects of childbearing potential must not be pregnant at screening.  Exclusion Criteria:  Receipt of prior therapies as defined in the protocol The following lymphoma types/manifestations are not eligible for this study: Burkitt's lymphoma (BL), Burkitt-like lymphoma (BLL), lymphoblastic lymphoma/leukemia (LBL), post-transplant lymphoproliferative disease (PTLD), primary mediastinal (thymic) large B-cell lymphoma (PMBL), lymphomas involving the central nervous system (CNS) or meninges History of autoimmune hemolytic anemia (AIHA) or idiopathic thrombocytopenic purpura (ITP). History of solid organ or allogeneic hematopoietic stem cell transplantation. Concomitant anticoagulation with the oral anticoagulants apixaban, betrixaban, rivaroxaban, and dabigatran. Use of a strong inhibitor or inducer of cytochrome P450 3A4 (CYP3A4) within 5 half-lives or 4 weeks prior to first dose of study treatment, whichever is shorter. Uncontrolled, significant intercurrent or recent illness Major surgery (eg, GI surgery) within 3 weeks before first dose of study treatment. Corrected QT interval calculated by the Fridericia formula (QTcF) > 470 ms per electrocardiogram (ECG). Pregnant or lactating females. Inability to swallow XL114 tablets. Diagnosis of another malignancy within 2 years before first dose of study treatment, except for superficial skin cancers, or localized, low-grade tumors deemed cured and not treated with systemic therapy