Inclusion Criteria for Enrollment:  A subject may participate in the study if all the following criteria is met:  Patients with CD19+ malignancies that are refractory to or relapsed after current standard treatment (including allogeneic or autologous HSCT) and not suitable for other treatment options, such as second-time HSCT. CD19+ malignancies include:  Relapsed/Refractory B-cell Acute Lymphoblastic Leukemia (ALL):  Refractory ALL is defined as failure to achieve CR at the end of induction. Relapsed ALL is defined as reappearance of blasts in the blood or bone marrow (≥ 5%) or in any extramedullary site after a CR.  Relapsed/Refractory B-cell originated Non-Hodgkin Lymphoma (NHL) including 1) de-novo diffuse large B-cell lymphoma or primary mediastinal large B-cell lymphoma, 2) large-B cell lymphoma transformed from indolent lymphomas, 3) follicular lymphoma of all grades, 4) mantle cell lymphoma, and 5) CD20(+) high-grade B-cell lymphomas. Refractory disease for lymphoma is defined as:  Progressive disease or stable disease lasting < 6 months, as best response to most recent chemotherapy regimen; or disease progression or recurrence < 12 months after prior autologous HSCT. Prior therapy must have included an anti-CD20 monoclonal antibody-containing regimen and an anthracycline-containing chemotherapy regimen For patients with transformed follicular lymphoma (TFL), prior chemotherapy for follicular lymphoma and subsequent refractory disease after transformation to DLBCL. At least one measurable lesion, demonstrating that the nodal lesion is ≥ 1.5 cm in the longest diameter or the extranodal lesion is ≥ 1.0 cm in the longest diameter, according to the Lugano Classification (2014). Patients must have received at least 2 prior lines of therapy. HSCT (allogeneic or autologous) can be accounted as one of the prior line therapy, and the subjects must have been at least 3 months from prior HSCT. Karnofsky Performance Scale ≥ 60 Patient able to provide written informed consent for participating in the study Age ≥ 20 years and ≤ 75 years old at the time of providing informed consent Patients shall be at least 3 weeks from the last cytotoxic chemotherapy before apheresis. Short-acting targeted therapies (e.g., tyrosine kinase inhibitors) must be stopped > 72 hours before apheresis. Monoclonal antibody use including Anti-CD20 therapy has been discontinued at least 4 weeks before leukapheresis and CAR-T cells infusion except for systemic inhibitory/stimulatory immune checkpoint therapy. Immune checkpoint therapy has been discontinued at least 3 half-lives before leukapheresis (e.g. ipilimumab, nivolumab, pembrolizumab, atezolizumab, OX40 agonists, 4-1BB agonists, etc.). Absolute lymphocyte count (ALC) ≥ 1.0x109/L and absolute number of CD3+ T cells (ATC) ≥ 0.3x109/L, absolute neutrophil count (ANC) ≥ 1.0 x109/L for lymphoma and ANC ≥ 0.5 x109/L for ALL, platelets ≥ 50.0 x109/L, hemoglobin ≥ 80.0 g/L within 7 days before apheresis.  Adequate organ function demonstrated by the following:  Renal: serum creatinine <2 x upper limit of normal (ULN) Hepatic: ALT/AST ≤ 2.5 x ULN or ≤ 5 x ULN if documented liver metastases, total bilirubin ≤ 1.5 mg/dL, except in subjects with Gilbert's Syndrome in whom total bilirubin must be ≤ 3.0 mg/dL. Cardiac: no clinically significant ECG findings, hemodynamically stable and LVEF ≥ 45% confirmed by echocardiogram Pulmonary: baseline oxygen saturation > 90% on room air 10. Not receiving anti-thymocyte globulin (ATG), alemtuzumab, or other T-cell immunosuppressive antibodies, donor-lymphocyte infusion or T-cell infusion for the past 3 weeks before apheresis; Negative serology for Anti-HTLV-I / HTLV-II (DHTLV I/II)  Exclusion Criteria for Enrollment  A subject who met any of the following criteria is not eligible to enter the study:  Received previous treatment with anti-CD19 therapy; Is with a history of CNS malignancy and/or active CNS diseases; Has previous or concurrent malignancies other than CD19+ malignancies; Has active neurological, autoimmune, or inflammatory disorders; Has clinically significant cardiac diseases, or cardiac arrhythmia not controlled with medical treatment; Has cardiac involvement with lymphoma; Has any active infections, conditions, and diseases that may interfere with the assessment of safety and efficacy of the study deemed by the investigator or designee; Received live vaccine within 6 weeks of the screening Received radiation therapy within 2 weeks of the planned CAR-T cells infusion; Is with positive serology for HIV; Is with positive hepatitis B or hepatitis C infection, defined as positive HBs Ag or positive Anti-HCV Ab; Active graft versus host disease (GVHD) ≥ grade 2 using the CIBMTR Acute GVHD Grading System or requiring systemic steroid therapy greater than physiologic dosing; Note: Overall grading of GVHD is based on the criteria published by Przepiorka et al., Bone Marrow Transplant 1995; 15(6):825-8, see the GVHD Grading and Staging table at CIBMTR Forms Instruction Manual (Last updated: 2020/03/10), page 301-303 (Available at https://www.cibmtr.org/manuals/fim, accessed on 08 Apr 2020). Use of investigational medicinal product within 30 days before the screening; Positive beta HCG in female of child-bearing potential (defined as not post-menopausal for 12 months) or history of previous surgical sterilization or lactating females. Patients with known allergy to mouse products or cetuximab.  Inclusion Criteria for Lymphodepletion and T-Cell Infusion:  Prior to Lymphodepletion (LD):  Patients must have no evidence of clinically significant infection; No acute neurological toxicity >grade 1 (with the exception of peripheral sensory neuropathy) prior to conditioning chemotherapy; No clinically significant cardiac dysfunction; Serum creatinine < 2x ULN; No evidence of grade ≥2 acute GVHD; Pulmonary: oxygen saturation > 90% on room air; Adequacy of T cells apheresis products to manufacture CAR-T product.  Prior to CAR-T cells infusion:  Patients shall be at least 4 weeks from the last cytotoxic chemotherapy (excluding the study mandated lymphodepleting chemotherapy) before infusion. Short-acting targeted therapies (e.g., tyrosine kinase inhibitors) must be stopped > 72 hours before infusion. At least 4 weeks from anti-thymocyte globulin (ATG), alemtuzumab, or other T-cell immunosuppressive antibodies, donor-lymphocyte infusion or T-cell infusion; Steroids, if given as GVHD therapy, must be stopped >72 hours prior to infusion. However, the following physiological replacement doses of steroids are allowed: < 6-12 mg/m2/day hydrocortisone or equivalent. Non-hematologic toxicity grade ≥2 (CTCAE version 5) related to the lymphodepleting chemotherapy until the toxicity has resolved to grade ≤1 and the subject is afebrile; No grade >2 neurologic, pulmonary, cardiac, gastrointestinal, renal, or hepatic (excluding albumin) toxicity; Adequacy of the CAR-T cells for infusion.  Exclusion Criteria For Lymphodepletion and T-Cell Infusion:  A subject who meets any of the following criteria should not undergo LD or infusion of CAR-T cells.  New onset of cardiac arrhythmia not uncontrolled with medications; Hypotension warrants the use of vasopressor; Active infections within 1 week prior to CAR-T infusion that necessitate the use of oral or intravenous anti-infective treatments; subjects with ongoing use of prophylactic antibiotics, antifungals, or antivirals are eligible as long as there is no evidence of active infection. Presence of CNS or neurological abnormalities; Received HSCT after screening or planned to receive HSCT during the study period; Any conditions not suitable for the CAR-T cells infusion in the PI or designee's judgement.