Natural Killer (NK) Cell Therapy for B-Cell Malignancies

Key Inclusion Criteria: * Diagnosis of B-cell lymphoma or B-ALL as described below: B-cell Lymphoma: * Histologically documented lymphomas expected to express CD19 and CD20 * Relapsed/refractory disease following at least two prior systemic treatment regimens, or relapsed after the autologous hematopoietic stem cell transplantation (HSCT) B-ALL: * Diagnosis of B-ALL that expected to express CD19 * Relapsed/refractory disease following prior systemic treatment regimens ALL SUBJECTS: * Provision of signed and dated informed consent form (ICF) * Age ≥ 18 years old * Stated willingness to comply with study procedures and duration * Eastern Cooperative Oncology Group (ECOG) performance status ≤1 * Adequate organ function as defined in the protocol * Donor specific antibody (DSA) to QN-019a: MFI \<= 2000 * At least 3 weeks after the last systemic immunochemotherapy treatment * The estimated survival days are expected to be over 3 months Key Exclusion Criteria: ALL SUBJECTS: * Females who are pregnant or lactating * Evidence of insufficient organ function as defined in the protocol * ECOG Performance Status ≥2 * Prior allogeneic hematopoietic stem cell transplant (HSCT) or allogeneic CAR-T/CAR-NK within 6 months of Day 1, or ongoing requirement for systemic GvHD therapy * Currently receiving or likely to require systemic immunosuppressive therapy * Known active central nervous system (CNS) involvement by malignancy. Non-malignant CNS disease such as stroke, epilepsy, or neurodegenerative disease * Clinically significant cardiovascular disease as defined in the protocol * Known HIV infection, active Hepatitis B (HBV) or Hepatitis C (HCV) infection * Donor specific antibody (DSA) to QN-019a: MFI \> 2000 * Other comorbid conditions and concomitant medications prohibited as per study protocol * Investigator-assessed presence of any medical or social issues that are likely to interfere with study conduct or may cause increased risk to subject