To find the highest tolerable dose of dualCAR-NK19/70 (a type of cell therapy) that can be given to patients who have B-cell lymphoma that is relapsed or refractory.

Primary Objectives:

--The primary objective is to determine the safety and identify the maximum tolerated dose (MTD) or recommended phase 2 dose (RP2D) of dualCAR-NK19/70 in patients with r/r B-cell lymphomas.

Hypothesis: DualCAR-NK19/70 will be safe, well-tolerated, and effective in patients with r/r B-cell lymphomas.

Secondary Objectives:

--The secondary objective is to determine the efficacy in adults with r/r LBCL and FL grade 3B treated at the MTD or RP2D of dualCAR-NK19/70. Although the clinical benefit of dualCAR-NK19/70 has not yet been established, the intent of offering this treatment is to provide a possible therapeutic benefit, and thus the patient will be carefully monitored for tumor response and symptom relief in addition to safety and tolerability. Secondary endpoints include overall response rate (ORR; including CR + PR) and CR rate as defined by the Lugano Classification response criteria for malignant lymphoma, DOR, PFS, and OS.

Exploratory Objectives:

--The exploratory objectives are to assess the cellular kinetics and pharmacodynamic effects of dualCAR-NK19/70 and to evaluate biomarkers associated with response, resistance, and toxicity after administration of dualCAR-NK19/70 in blood and tumor samples.

Inclusion Criteria:

1. Voluntarily participate in the study and sign the informed consent;

2. Age 18-75, male and female;

3. Histologically confirmed diffuse large B-cell lymphoma (DLBCL), transformed follicular lymphoma (tFL), primary mediastinal B-cell lymphoma (PMBCL), mantle cell lymphoma (MCL), and other Indolent B-cell NHL transforming types:

   （A） Relapsed or Refractory DLBCL and tFL after 2 lines Immunotherapy or chemotherapy ; （B） Definition of Refractory large B cell lymphoma (SCHOLAR - 1 Research Standard) : disease progression after more than 4 courses of standard Immunotherapy or chemotherapy; Or the time of disease stabilization ≤ 6 months; Or disease progression or recurrence within 12 months after autologous hematopoietic stem cell transplantation (auto-HSCT); （C） Relapsed or Refractory MCL must be 1 line with immune chemotherapy; BTK inhibitors are resistant or intolerant as 2-line therapy; （D） Relapsed or Refractory disease after chemotherapy including rituximab and anthracycline.

4. There was at least one measurable lesion with the longest diameter ≥ 1.5cm;

5. Estimated life expectancy of more than 12 weeks other than primary disease;

6. Previously confirmed diagnosis as CD19+ or CD70+ B-NHL.

7. Eastern Cooperative Oncology Group (ECOG) performance status of 0 - 3.

8. Adequate reserve of organ function:

   （A） Serum alanine aminotransferase (ALT) / aspartate aminotransferase (AST) ≤2.5 times the Upper Limit of Normal (ULN) for age; （B） A creatinine clearance (as estimated either by a direct urine collection or Cockcroft-Gault Equation) > 60mL/min; （C） Total bilirubin and alkaline phosphatase ≤1.5 times the Upper Limit of Normal (ULN) for age; （D） glomerular filtration rate > 50 ml/min （E） Cardiac ejection fraction (EF) ≥ 45% as determined by an echocardiogram (ECHO) or Multigated Radionuclide Angiography (MUGA); （F） Baseline oxygen saturation >92% on room air （G） Absolute neutrophil count > 1000/μL, Platelet count > 45,000/μL ,Hemoglobin > 80g/L;

9. Once previous autologous hematopoietic stem cell transplantation (auto-HSCT) is allowed;

10. For systemic therapy(Such as systemic chemotherapy, systemic radiotherapy and immunotherapy), at least 3 weeks，for Targeted drug therapy alone，at least 2 weeks，must have elapsed at the time of cell infusion;

11. Either having failed or Relapsed after CAR-T therapy at 3 months of assessment;

12. Subjects of child-bearing or child-fathering potential must be willing to practice birth control from the time of enrollment on this study until the follow-up period of the study. Women of childbearing potential must have a negative serum or urine pregnancy test.

13. The viral load of severe coronavirus disease 2019 (COVID-19) is undetectable per quantitative PCR and/or nucleic acid testing for two tests.

Exclusion Criteria:

1. Allergic to any of the components of cell products;
2. Previous or concurrent of other type of maligant tumors;
3. Acute GvHD or generalized chronic GvHD with grade II-IV (Glucksberg standard) after previous autologous hematopoietic stem cell transplantation (auto-HSCT); Or receiving of anti-GVHD therapy;
4. Known history of systemic gene therapy within the prior 3 months;
5. Active systemic fungal, viral, or bacterial infection (except for simple urinary tract infections and bacterial pharyngitis), however, Preventive treatment is permitted;
6. Known history of infection with hepatitis B (HBsAg positive, but HBV-DNA<1000 is not excluded) or hepatitis C virus (including virus carriers), syphilis and other acquired and congenital immunodeficiency diseases, including but not limited to HIV infection;
7. Class III or IV heart failure as defined by the New York Heart Association;
8. Persisting toxicities (>grade 1, except for clinically non-significant toxicities such as alopecia, fatigue, and anorexia) due to prior trerapy;
9. Known history of active seizures or presence of seizure activities or other central nervous system disease;
10. Have evidence of central nervous system lymphoma(CNS lymphoma) on CT or MRI;
11. Breast-feeding woman;
12. Any circumstances that possibly increase the risk of subjects or interfere with study results, which judged by investigator.