A Study Evaluating Safety and Efficacy of C-CAR039 Treatment in NHL Subjects

Inclusion Criteria: * 1\. Volunteered to participate in this study and signed informed consent * 2\. Age 18-75 years old, male or female * 3\. CD19 or CD20 positive DLBCL (including PMBCL and tFL), FL and MCL confirmed by cytology or histology according to WHO2016 criteria. For CD20-positive subjects, they should have received at least one regimen containing anti-CD20-targeted therapy (such as rituximab). If they do not complete the regimen due to intolerance, the cause should be recorded. * 4\. Relapsed or refractory disease after ≥ 2 lines (for FL, at least 3 lines) of standard therapy or relapsed after autologous stem cell transplantation (ASCT) * 5\. At least one measurable lesion (LDi ≥ 1.5 cm); * 6\. At least two weeks from last treatment (radiation, chemotherapy, mAb, etc) to apheresis; * 7\. LVEF≥ 50% (ECHO) * 8\. No active pulmonary infections, normal or mild impaired pulmonary function and SpO2≥92% * 9\. Laboratory criteria: ANC≥1.0×109/L; Platelets≥50×109/L; Serum total bilirubin ≤1.5x ULN; Creatinine≤ ULN; AST and ALT≤3x ULN * 10\. No contraindications of apheresis; * 11\. Expected survival ≥ 3months * 12\. ECOG score 0 or 1 Exclusion Criteria: * 1\. Have a history of allergy to cellular products; * 2\. According to the NYHA cardiac function grading standards, patients with grade III or IV cardiac dysfunction; * 3\. A history of craniocerebral trauma, disturbance of consciousness, epilepsy, cerebrovascular ischemia, cerebrovascular hemorrhagic disease, etc.; * 4\. Patients with central nervous system involvement; * 5\. Patients with autoimmune diseases, immunodeficiency or other conditions requiring immunosuppressive therapy; * 6\. Received allogeneic hematopoietic stem cell transplantation before; * 7\. Previous use of any CAR T cell product or other genetically modified T cell therapy; * 8\. Autologous stem cell transplantation within 6 weeks before infusion; * 9\. Severe active infections (except for simple urinary tract infections, bacterial pharyngitis), or currently undergoing intravenous infusion of antibiotics. However, prophylactic antibiotic, antiviral and antifungal infection treatments are permissible; * 10\. Live vaccination within 4 weeks prior to apheresis; * 11\. People infected with HIV, HBV, HCV and TPPA/RPR, and carriers with HBV; * 12\. A history of alcohol abuse, drug use or mental illness; * 13\. Subjects who are not sterilized and have any of the following conditions: 1. are pregnant/lactating; or 2. planned pregnancy during the trial; or 3. being fertile and unable to use effective contraception; * 14\. Severe hypersensitivity to fludarabine or cyclophosphamide; * 15\. A history of other primary cancers other than the following: 1. Non-melanoma tumors such as basal cell carcinoma of the skin that are cured by excision 2. Cured in situ cancers such as cervical, bladder, or breast cancer * 16\. The investigators consider that the subject has other conditions that are not suitable for this trial.