A Phase 1/2 Study To Evaluate ASN002 In Relapsed/Refractory Lymphoma And Advanced Solid Tumors

Inclusion Criteria: * Written informed consent obtained prior to any study-related procedure being performed; * Male or female subjects at least 18 years of age at the time of consent; * Eastern Cooperative Oncology Group (ECOG) Performance Status 0-2; * Recovered from the reversible effects of prior antineoplastic therapy (with the exception of alopecia and Grade 1 neuropathy). * Screening blood counts of the following: Absolute neutrophil count ≥ 1000/μL, Platelets ≥ 75,000/μL, Hemoglobin ≥ 8 g/dL (with transfusion support); * Screening chemistry values of the following: Alanine aminotransferase (ALT) and aspartate transaminase (AST) ≤ 3.0 × upper limit of the normal (ULN), total bilirubin ≤ 1.5 × ULN, Creatinine ≤ 1.5 × ULN; * At screening, life expectancy of at least 3 months; * Subject is willing and able to comply with all protocol required visits and assessments; * Male and female subjects of child-bearing potential must agree to use medically acceptable methods of birth control throughout the study and for thirty (30) days after the last dose of study medication. * (Part A only) Histologically or cytologically confirmed metastatic and/or advanced solid tumors or lymphomas for which no standard therapy exists, or who are not eligible for standard treatment. Subjects must have received at least one prior therapy for their malignancy; * (Part B only) Histologically confirmed DLBCL/MCL/FL/PTCL/MF/CLL on the basis of excisional lymph node or extranodal tissue biopsy; diagnosis of relapsed/refractory disease defined as 1) recurrence of disease after a Complete Response (CR), or 2) Partial Response (PR), Stable Disease (SD) at completion of treatment regimen preceding entry into study, subjects must not be candidates for standard therapy, subjects who have not received Stem Cell Translplant (SCT) must be ineligible to receive SCT. Exclusion Criteria * Have received prior chemotherapy regimens within 4 weeks of Day 1; * Have received prior treatment with monoclonal antibodies within 6 weeks of first dose of Day 1; * Have had major surgery within 30 days prior to the start of Day 1; * Received any investigational treatment within 4 weeks prior to the start of study medication; * Have had an infection requiring the use of parenteral antibiotics within 14 days prior to the start of Day 1; * Have known central nervous system metastasis or Central Nervous System lymphoma; * Is receiving high dose corticosteroids (\>10 mg prednisone daily or equivalent); * Has known bleeding diathesis that would be a safety risk; * Has a history of other malignancy within the 3 years prior to screening, except adequately treated basal cell or squamous cell carcinoma of the skin, or carcinoma in-situ; * Has difficulty swallowing medications, or known history of malabsorption syndrome; * Has a serious concurrent medical condition, such as: congestive heart failure New York Heart Association (NYHA) class III or IV or uncontrolled hypertension at screening, 12-Lead electrocardiogram (ECG) abnormalities considered by the investigator to be clinically significant including myocardial infarction, angioplasty, or cardiac stent placement within the last 6 months, HIV infection, known Hepatitis B or C infection. Subjects at high risk for Hepatitis B or C infection should have serology testing to rule out infection, a medical condition requiring the therapeutic use of anticoagulants. * Known hypersensitivity to ASN002 or its excipients; * Prior participation, i.e., receipt of study medication, in this study; * Any condition that, in the opinion of the investigator, would impair the subject's ability to comply with study procedures; * Female subjects that are pregnant or lactating. * Part B only: Prior treatment with SYK or Janus Kinase (JAK) inhibitors, except MF subjects.