Inclusion Criteria:  Signed informed consent form (ICF) Age 18 Years to 75 Years  Pathological diagnosis of refractory/relapsed CD4+ T lymphocyte tumor (one of the following):  a. T-cell Non-Hodgkin lymphoma(T-NHL)：The best response is progressive disease(PD) or stable disease(SD) after at least 1 prior line of therapy（at least 2 complete cycle of therapy） b. T-cell Acute lymphoblastic leukemia(T-ALL)：The best response is not complete response(CR) after induction therapy  Measurable disease is necessary at Screening Life expectancy ≥ 3 months Eastern Cooperative Oncology Group (ECOG) Performance Status grade of 0 -2.  The screening phase clinical laboratory values meet the following criteria. Laboratory test(s) may be repeated once, to determine if the subject qualifies for study participation :  Blood routine:  HGB≥6g/dL；PLT≥20×10^9/L; ANC≥1.0×10^9/L; LY≥0.3×10^9/L  Blood biochemical parameters:  Aspartate and alanine aminotransferases (AST, ALT) ≤ 2.5 times ULN (in the presence of liver metastasis, AST and ALT≤5 times ULN) Serum creatinine (Scr) ≤ 1.5 times ULN, estimated glomerular filtration rate (eGFR) > 60mL/min (only when Scr>1.5 times ULN) Total bilirubin ≤ 1.5 times of the normal upper limit (ULN) International Normalized Ratio (INR) ≤ 1.5 times ULN, PT≤ 1.5 times ULN, APTT≤ 1.5 times ULN  Exclusion Criteria:  Prior treatment with CAR-T therapy directed at any target. Any therapy that is targeted to CD4. Prior treatment with an allogeneic stem cell transplant  Any malignancy besides the T lymphocyte tumor categories under study, exceptions include  Any other malignancy curatively treated and disease-free for at least 2 years prior to enrollment History of non-melanoma skin cancer with sufficient treatment and currently no evidence of recurrence Those who are positive for any index of hepatitis B surface antigen (HBsAg), hepatitis B virus deoxyribonucleic acid (HBV DNA), hepatitis C antibody (HCV-Ab), hepatitis C virus ribonucleic acid (HCV RNA), and human immunodeficiency virus antibody (HIV-Ab)  The following cardiac conditions:  New York Heart Association (NYHA) stage III or IV congestive heart failure Myocardial infarction or coronary artery bypass graft (CABG) 6 months prior to enrollment History of clinically significant ventricular arrhythmia or unexplained syncope, not believed to be vasovagal in nature or due to dehydration History of severe non-ischemic cardiomyopathy Impaired cardiac function (LVEF <45%) as assessed by echocardiogram or multiple-gated acquisition (MUGA) scan (performed ≤8 weeks of apheresis)  Prior antitumor therapy as follows, prior to apheresis:  Targeted therapy, epigenetic therapy, or treatment with an investigational drug or used an invasive investigational medical device within 14 days or at least 5 half-lives, whichever is less. Monoclonal antibody treatment for multiple myeloma within 21 days. Cytotoxic therapy within 14 days. Radiotherapy within 14 days.  Participated in other clinical trials within 30 days.  8. Toxicity from previous anticancer therapy must resolve to baseline levels or to Grade 1 or less except for alopecia or peripheral neuropathy.  9. With central nervous system involvement. 10. Serious underlying medical condition, such as:  a. Evidence of serious active viral, bacterial, or uncontrolled systemic fungal infection b. Active or unstable autoimmune diseases or autoimmune diseases that have been suffered within 3 years and have the possibility of recurrence c. Overt clinical evidence of dementia or altered mental status  11. Pregnant or breast-feeding, or planning to become pregnant while enrolled in this study or within 100 days after receiving study treatment.  12. Plans to father a child while enrolled in this study or within 100 days after receiving study treatment.  13. With obvious hemorrhagic tendency such as gastrointestinal hemorrhage, coagulation disorders and hypersplenism 14. Oxygen is needed to maintain sufficient blood oxygen saturation(≥95%) 15. Suffer from chronic diseases that require treatment with systemic corticosteroids or other immunosuppressive agents ,Received a cumulative dose of corticosteroids equivalent to ≥20 mg/day of prednisone within 7 days prior to apheresis 16. CNS diseases with clinical significance in the past or at the time of screening 17. Vaccinated with live, attenuated vaccine within 4 weeks prior to apheresis 18. Major surgery within 2 weeks prior to apheresis, or has surgery planned during the study or within 2 weeks after study treatment administration. (Note: subjects with planned surgical procedures to be conducted under local anesthesia may participate.) 19. Known life threatening allergies, hypersensitivity, or intolerance to LCAR-T2C CAR-T cells or its excipients, including DMSO (refer to Investigator's Brochure) 20. Presence of any condition that, in the opinion of the investigator, would prohibit the patient from undergoing treatment under this protocol