Study of AXT-1003 in Adult Subjects With Relapsed/Refractory Non-Hodgkin Lymphomas

Inclusion Criteria: 1. Female or male subjects aged ≥ 18 years. 2. Histopathological diagnosis of relapsed/refractory non-Hodgkin lymphoma \[R/R NHL\] (except for CLL/SLL), who have progressed after treatment with approved therapies or who have no access to approved or standard therapies. Note 1: Refractory is defined as failure to: 1. Achieve complete response after first-line therapy 2. Reach at least partial response after second-line therapy or beyond. Note 2: Subjects must be considered hematopoietic cell transplantation (HCT) ineligible during screening due to disease status (active disease), comorbidities, or other factors; the reason for HCT ineligibility must be clearly documented. 3. For dose expansion part: Subjects with pathologically confirmed R/R NHL by the local pathologist/investigators are enrolled. Most of the enrolled subjects are confirmed with R/R PTCL subtype. Local histological diagnosis will be used for eligibility determination. Subjects with PTCL are eligible according to 2016 World Health Organization (WHO) classification, including but not limited to the following subtypes: 1. PTCL, not otherwise specified. 2. Anaplastic large cell lymphoma, anaplastic lymphoma kinase (ALK) positive 3. Anaplastic large cell lymphoma, ALK negative 4. Angioimmunoblastic T-cell lymphoma 5. Extranodal NK-/T-cell lymphoma, nasal type The subjects enrolled in the dose expansion part should be progressed after treatment with approved therapies or who have no access to approved or standard therapies. 4. Eastern Cooperative Oncology Group performance status scale 0 to 1. 5. Have a life expectancy of at least 3 months. 6. Have measurable disease as defined by Lugano 2014 criteria, subjects must have measurable lesions (nodal lesion with any long diameter \> 1.5 cm, or extranodal lesion with any long diameter \> 1.0 cm) (not mandatory for the dose escalation stage). 7. Willing to provide archived or fresh tumor tissue samples that are sufficient for EZH2 status detection (not mandatory). 8. Adequate organ function assessed within 7 days prior to study drug administration. 9. Bone marrow function: absolute neutrophil count (ANC) ≥ 1.0 × 109/L without growth factor support (filgrastim or) for at least 14 days; Hb ≥ 9.0 g/dL (may receive transfusion), platelets ≥ 75 × 109/L (Evaluated after at least 7 days since last platelet transfusion). 10. Hepatic function: serum total bilirubin ≤ 1.5 × upper limit of normal (ULN) except for unconjugated hyperbilirubinemia of Gilbert's syndrome; alkaline phosphatase (in the absence of bone disease) ALT/AST ≤ 3.0 × ULN (≤ 5 × ULN if subject has liver metastases). 11. Renal function: calculated creatinine clearance ≥ 60 mL/min (Cockcroft-Gault method). 12. Time between prior anticancer therapy and first dose of AXT-1003 as below: 1. Cytotoxic chemotherapy-at least 21 days or 3.5 half-lives of prior treatment, whichever occurs later. 2. Non-cytotoxic chemotherapy (eg, small molecule inhibitor)-at least 14 days or 3.5 half-lives of prior treatment, whichever occurs later. 3. Nitrosoureas-At least 6 weeks or 3.5 half-lives of prior treatment, whichever occurs later. 4. Monoclonal antibody (ies)-at least 28 days 5. Radiotherapy-At least 14 days from local site radiation therapy/at least 6 weeks from prior radioisotope therapy/at least 12 weeks from 50% pelvic or total body irradiation. 6. High dose therapy with autologous hematopoietic cell infusion-at least 60 days. 7. High dose therapy with allogeneic transplant-At least 90 days (if graft versus host disease \[GVHD\] is present, must be Grade \< 2) and no prohibited medications. Note: Starting at Cycle 1 Day 1, subjects may receive no more than 10 mg of prednisone daily (or equivalent corticosteroid) when used for treatment of lymphoma related symptoms, with the intent to taper by the end of Cycle 1. 13. Male subjects must have had a successful vasectomy (with confirmed azoospermia), or they and their female partner must meet the criteria above (ie, not of childbearing potential or practicing highly effective contraception and use a condom throughout the study period and for 3 months after study drug discontinuation). Non-vasectomized male subjects must also agree to refrain from donating sperm from first dose of AXT-1003 until 3 months following the last dose of AXT-1003. 14. Females must not be lactating or pregnant at screening or baseline (as documented by a negative beta-human chorionic gonadotropin test with a minimum sensitivity of 25 IU/L or equivalent units of beta-human chorionic gonadotropin). A separate baseline assessment is required if a negative screening pregnancy test was obtained more than seven days before the first dose of study drug. All females will be considered as childbearing potential unless they are postmenopausal (at least 12 months consecutively amenorrheic, in the appropriate age group, and without other known or suspected cause) or have been sterilized surgically (ie, bilateral tubal ligation, total hysterectomy, or bilateral oophorectomy, all with surgery at least 1 month before dosing). Females of childbearing potential must not have had unprotected sexual intercourse within 30 days prior to study entry and must agree to use a highly effective method of contraception, from the last menstrual period prior to randomization, during treatment cycles, and for 30 days (will be re estimated after PK profile is known) after the final dose of study drug and have a male partner who uses a condom. Highly effective contraception includes: 1. Double barrier methods of contraception such as condom plus diaphragm or cervical/vault cap with spermicide. 2. Placement of an intrauterine device. 3. Established hormonal contraceptive methods: oral, injectable, or implant. Females who are using hormonal contraceptives must have been on a stable dose of the same hormonal contraceptive product for at least 4 weeks prior to dosing and must continue to use the same contraceptive during the study and for 30 days after study drug discontinuation. Female subjects exempt from this requirement if they practice total abstinence or have a male partner who is vasectomized. If currently abstinent, the subject must agree to use a highly effective method of contraception as described above if they become sexually active during the treatment cycles, and for 30 days after study drug discontinuation. 15. Signed ICF and willing to comply with all aspects of the protocol. Exclusion Criteria: 1. Diagnosis of precursor B-cell lymphoblastic leukemia/lymphoma, precursor T-cell lymphoblastic leukemia/lymphoma, precursor NK cell lymphoblastic leukemia/lymphoma. 2. Diagnosis of CLL, SLL. 3. Diagnosis of Burkitt lymphoma. 4. Received treatment with compounds with the same mechanism of action (EZH2 inhibitor, EZH1/EZH2 inhibitor etc.). 5. Central nervous system infiltration. 6. Clinically significant GVHD or GVHD requiring systemic immunosuppressive prophylaxis or treatment. 7. Uncontrolled or significant cardiovascular disease, including: 1. Evidence of prolongation of QT/QTc interval (eg, repeated episodes of QT corrected for heart rate using Fridericia's method \> 470 msec) (average of triplicate determinations). 2. Diagnosed or suspected long QT syndrome or known family history of long QT syndrome. 3. History of clinically relevant ventricular arrhythmias, such as ventricular tachycardia, ventricular fibrillation, or Torsade de Pointes. 4. Uncontrolled arrhythmia (subjects with asymptomatic, controllable atrial fibrillation may be enrolled) or asymptomatic persistent ventricular tachycardia. 5. History of second- or third-degree heart block. Subjects with a history of heart block may be eligible if they currently have pacemakers and have no history of fainting or clinically relevant arrhythmia with pacemakers within 6 months prior to screening. 6. Myocardial infarction within 6 months prior to screening. 7. Angioplasty or stent craft implantation within 6 months prior to screening. 8. Uncontrolled angina pectoris within 6 months prior to screening. 9. New York Heart Association Class 3 or 4 congestive heart failure. 10. Coronary/peripheral artery bypass graft within 6 months prior to screening. 11. Uncontrolled hypertension (resting systolic blood pressure \> 160 mmHg or diastolic blood pressure \> 110 mmHg). 12. Complete left bundle branch block. 8. Venous thrombosis or pulmonary embolism within the last 3 months before starting treatment. 9. Major surgery within 4 weeks before the first dose of study drug. Note: Minor surgery (e.g, minor biopsy of extracranial site, central venous catheter placement, shunt revision) is permitted within 3 weeks prior to enrolment. 10. Known or suspected hypersensitivity to AXT-1003 or any of the excipients. 11. Inability to take oral medication, or malabsorption syndrome or any other uncontrolled gastrointestinal condition (eg, nausea, diarrhea, or vomiting) that might impair the bioavailability of AXT-1003. 12. Use of known median or potent Cytochrome P450 3A4 (CYP3A4) inducers/inhibitors or P glycoprotein (P-gp) inhibitors. 13. Subjects unwilling to remove seville oranges, grapefruit juice and grapefruit from their diet. 14. History of other malignancies prior to enrolment; except for subjects with basal cell carcinoma of skin, squamous cell carcinoma of skin, cervical carcinoma in situ, or other carcinomas in situ who have undergone possible curative treatment and do not have disease recurrence within 5 years since starting the treatment. 15. Any prior treatment-related (ie, chemotherapy, immunotherapy, radiotherapy, target therapy or other study clinical therapy) clinically significant toxicities that have not resolved to Grade ≤ 1 per CTCAE version 5.0 or prior treatment-related toxicities that are clinically unstable and clinically significant at time of enrolment. 16. Active infection requiring systemic therapy. 17. Has known history of chronic infection with hepatitis B virus (hepatitis B surface antigen positive) or hepatitis C virus (detectable antihepatitic C circulating viral RNA). 18. Immunocompromised subjects, including subjects known to be infected with human immunodeficiency virus, and tuberculosis. 19. Females who are pregnant or breastfeeding. 20. Any other major illness that, in the investigator's judgment, will substantially increase the risk associated with the subject's participation in this study.