This study is designed to evaluate the safety, tolerability, pharmacokinetic profile, and antitumor efficacy of DZD8586 in participants with relapsed or refractory B-NHL.

Inclusion Criteria:

1. All participants must provide a signed and dated written informed consent form prior to any study-specific procedures, sampling, and analysis.
2. Male and female participants must be ≥ 18 years of age when signing the informed consent form.
3. ECOG performance status score of 0 - 2 points and no disease deterioration in the past two weeks.
4. Participants with relapsed or refractory B-NHL must be cytologically or histologically confirmed.
5. Adequate bone marrow reserve (no blood transfusion within 7 days of the pre-enrollment visit, and no use of any stimulating factor or erythropoietin) and organ function.
6. Participants should be able to follow the requirements of this study for medication use and follow-up.
7. Female spouses (partners) of male participants who may become pregnant should use barrier contraception (such as condoms) during the participants' participation in the trial and within 6 months after the end of dosing. Male participants should also refrain from donating sperms during participation in the trial and within 6 months after the end of dosing.
8. Female participants should use adequate contraception such as abstinence, tubal ligation, use of hormonal contraception with a known lower risk of drug-drug interaction [levonorgestrel intrauterine device (Mirena), medroxyprogesterone injection (Depo Provera)], copper-containing intrauterine device, and partner's vasectomy during the trial and within 3 months after the end of the trial.

Exclusion Criteria:

1. Have unresolved adverse drug reactions (except for alopecia) of higher than grade 1 (as defined by CTCAE v5.0) before the start of dosing in the study.

2. A history of anticancer treatment within washout period as defined in the protocol.

3. Participants with B-NHL other than CNSL who have central nervous system or intraocular lymphoma lesions.

4. Participants with CNSL who have the following health conditions:

   1. Unable to cooperate with a lumbar puncture or cerebrospinal fluid test.
   2. Involvement of sites outside the CNS requiring systemic therapy.
   3. Participants with condition requiring systemic glucocorticoid therapy at a dose of > 8 mg/day (dexamethasone equivalent dose); or participants requiring immunosuppressant or biologic therapy.

5. Active infectious diseases, including HBC, HCV, HIV, TB, etc.

6. Abnormal heart and lung function.

7. Refractory nausea and vomiting not well controlled by supportive care, chronic gastrointestinal disease, dysphagia, or previous surgical resection of bowel segments that may interfere with adequate drug absorption.

8. Participants diagnosed with other malignancies apart from B-cell lymphoma within the past 5 years. However, participants may also be enrolled if the current evidence shows that the participant has been clinically cured and the investigator believes that the potential benefit of treatment with DZD8586 outweighs the potential risk.

9. Participants with hypersensitivity to DZD8586 pharmaceutical excipients or other chemical analogs.

10. Participants with serious or poorly controlled systemic diseases as judged by the investigator or other evidence, including poorly controlled hypertension and active bleeding disorders.

11. Personnel involved in the planning and implementation of this study (only applicable to employees of the sponsor and study site).

12. Female participants who are breastfeeding or pregnant.

13. Participants who have taken DZD8586.

14. Participants should not participate in the study if they are considered by the investigator to be unlikely to comply with study procedures, restrictions, and requirements.