CARTALL: Chimeric-Antigen Receptor (CAR) T-Cell Therapy for Relapsed/ Refractory T-Lineage Acute Lymphoblastic Leukaemia

Inclusion Criteria: * Diagnosis/ Disease define as: 1. Relapsed T-cell acute lymphoblastic leukaemia/ lymphoma as defined by: Bone marrow disease = or \> 0.01% by MRD as determined by flow cytometry Or CNS disease as defined as \> 5 WBCs/ uL in CSF with morphological evidence of blasts or biopsy proven recurrence in the eye or brain Or Extramedullary relapse as defined by morphological evidence of blasts in the testis or any other extramedullary sites 2. Induction failure as defined by: MRD = or \> 1% by flow cytometry at the end of induction on day 33 Or Failure to achieve morphological remission defined as \> 5% blasts after standard induction chemotherapy 3. Refractory disease as defined by: MRD = or \> 0.01% by flow cytometry or molecular methods during 2 or more timepoints after induction therapy * Minimum level of pulmonary reserve defined as Grade ≤ 1 dyspnoea and oxygen saturation (SpO2) of \> 95% on room air * Left ventricular systolic function (LVSF) ≥ 28% confirmed by echocardiogram, or left ventricular ejection fraction (LVEF) ≥ 45% confirmed by echocardiogram within 3 months of screening * Karnofsky (age ≥ 16 years) or Lansky (age \< 16 years) performance status ≥ 50 at screening * Normal Age-adjusted eGFR Creatinine Clearance within 3 months of screening * Alanine aminotransferase ≤ 5 times the upper limit of normal for age * Patients with \> 99% CD7 expression on blast cells will be eligible for anti-CD7 PEBL-CAR-T cell infusion. Exclusion Criteria: * Failure to meet any of the inclusion criteria * Patients who test positive on urine pregnancy testing and are pregnant or are lactating * Concomitant genetic syndromes associated with bone marrow failure states, such as Fanconi anaemia, Kostmann syndrome, Schwachman syndrome, or any other bone marrow failure syndrome with the exception of Down syndrome * Prior malignancy, except carcinoma in situ of the skin or cervix treated with curative intent and no evidence of active disease * Active or latent hepatitis B or hepatitis C infections within 8 weeks of screening, or any uncontrolled infection at screening * Positive Human Immunodeficiency Virus (HIV) test within 8 weeks of screening * Grade 2 to 4 acute graft-vs-host disease (GVHD) or extensive chronic GVHD * Received an investigational medicinal product within 30 days of screening * Central nervous system : Uncontrolled seizures or status epilepticus; increased intra-cranial pressure as evidenced by papilledema and CSF opening pressure \> 20 cm water; decreased conscious state (any cause)