Assessing an Oral Bruton Tyrosine Kinase Inhibitor, DZD9008 in Patients Who Have Non-Hodgkin B-cell Lymphoma (WU-KONG3)

Inclusion criteria: * Aged at least 18 years old. * Patients must be willing and able to participate in all required evaluations and procedures. * Patients must be able to provide a signed written informed consent. * With documented histologically confirmed diagnosis of CLL/SLL, MCL or MZL and have least 1 measurable site of disease. Subjects must have relapsed, or are refractory or intolerant to \>= 2 lines of prior therapy, and without preferred alternative treatment as judged by investigator. For Part B, subjects should be either BTK inhibitor treatment naive or intolerant to prior BTK inhibitor within 6 months on treatment. * Eastern Cooperative Oncology Group (ECOG) performance status 0-2. * Predicted life expectancy ≥ 12 weeks. * Adequate organ system functions. Exclusion criteria: * Prior malignancy requires active treatment within 2 to 3 years. * A life-threatening illness, medical condition or organ system dysfunction. * Radiotherapy with a limited field of radiation for palliation within 1 week of the screening. * Major surgery within 4 weeks before screening. * Prior treatment with any onco-immunotherapy within 4 weeks before screening. * Subjects require immediate cytoreduction. * Any history of Richter's transformation. * Central nervous system (CNS) involvement unless previous treated and asymptomatic. * Requires anticoagulation therapy with Warfarin, heparin. * Known history of human immunodeficiency virus (HIV); Positive Hepatitis B surface antigen (HbsAg) or positive HCV antibodies; any other uncontrolled active systemic infection. * Any of the following cardiac criteria: (1) mean resting corrected QT interval (QTcF) \> 470 msec obtained from 3 electrocardiograms (ECGs). (2) prior history of atrial fibrillation. (3) any factors that increase the risk of QTcF prolongation, such as heart failure, hypokalemia, congenital long QT syndrome, family history of long QT syndrome or unexplained sudden death under 40 years of age in first degree relatives or any concomitant medication known to prolong the QT interval * History of stroke or intracranial haemorrhage. * Past medical history of interstitial lung disease, drug-induced interstitial lung disease, radiation pneumonitis which required steroid treatment, or any evidence of clinically active interstitial lung disease * Refractory nausea and vomiting, chronic gastrointestinal diseases, inability to swallow the formulated product or previous significant bowel resection. * History of hypersensitivity. * Receiving (or unable to stop using) medications or herbal supplements known to be potent inhibitors or inducers of CYP3A. * Grapefruit, grapefruit juice, and orange marmalade (made with Seville oranges) should be excluded. * Women who are pregnant or breast feeding * Judgment by the investigator that the patient should not participate in the study if the patient is unlikely to comply with study procedures, restrictions and requirements * Previous allogenic bone marrow transplant.