Allogeneic CARCIK-CD19 in Adults/Pediatric B-cell NHL or Chronic Lymphocytic Leukemia

Inclusion Criteria: criteria apply: 1. Able and willing to provide written informed consent and to comply with the study protocol according to International Conference on Harmonization (ICH) and local regulations. 2. Ineligibility to commercially available CAR-T cells 3. Age limits: children (1-17 years old) and adults (≥18 years old) 4. Availability of an at least haploidentical (i.e. 4/8 HLA matched by allele typing) familial donor willing to and eligible for blood donation 5. Histologically-confirmed mature B-cell neoplasia (NHL), according to according to WHO 2021 classification: • Eligible histologies include: indolent \[follicular lymphoma (FL) or marginal zone lymphoma (MZL) nodal; extra-nodal; or splenic\] or aggressive \[diffuse large B-cell lymphoma (DLBCL), primary mediastinal large B-cell lymphoma (PMBL), high-grade B cell lymphoma with MYC and BCL2 rearrangements (double-hit lymphoma), mantle cell lymphoma (MCL), including transformed B-cell NHL\], CLL or lymphocytic lymphoma (LL). high-grade B cell lymphoma (HGBCL) NOS. Additional histologies including Burkitt lymphoma and Richter syndrome will be considered upon review with Sponsor. 6. Relapsed after or refractory to at least two prior lines of treatment, and no available treatment options that are expected to prolong survival (e.g. chemotherapy or high-dose chemotherapy/stem cell transplantation, commercially available CART cell therapy or other standard treatment) or patients refusing such treatments 7. At least one measurable target lesion, measurable as defined by Lugano 2014 classification (nodal: \> 1.5 cm longest transverse diameter; extra-nodal: \> 1 cm longest transverse diameter) by computerized tomography (CT) scan or presence of assessable disease (i.e. bone marrow or spleen) 8. Eastern Cooperative Oncology Group (ECOG) performance status equal to 2 or less for subject ≥ 16 years of age, or Lansky \>50 for subjects \< 16 years of age 9. Adequate cardiac and pulmonary function: ejection fraction (EF) by echo or MUGA \>40% and radial artery (RA) oxygen saturation \>92%. 10. Life expectancy (in the opinion of the Investigator) of \> 12 weeks 11. Adequate liver function: * Total bilirubin ≤ 2.0x ULN (≤ 3x ULN in patients with Gilbert's syndrome or documented liver involvement) * AST (aspartate aminotransferase) /ALT (alanine aminotransferase) 3x ULN or 5x for patients with evidence of liver involvement with lymphoma 12. Adequate bone marrow function to receive lymphodepleting chemotherapy at investigator judgment. 13. Adequate renal function: creatinine ≤1.5x ULN or creatinine clearance (CrCl) calculated by Cockcroft-Gault formula of ≥50 mL/min for adult patients in whom, in the Investigator's judgment, serum creatinine levels do not adequately reflect renal function. For children, CrCl will be calculated by local institutional standard. 14. Females of childbearing potential (FCBP) subjects must: * Have a negative pregnancy test as verified by the local investigator * Either commit to true abstinence from heterosexual contact or agree to use, and be able to comply with, effective contraception without interruption from screening until at least 12 months following CARCIK-CD19 infusion and until CAR positive viable T cells are no longer present by quantitative polymerase chain reaction (qPCR) on two consecutive tests. * Contraception methods must include one highly effective method including: surgical female sterilization, use of oral (estrogen and progesterone), injected, or implanted hormonal methods of contraception or placement of an intrauterine device (IUD) or intrauterine system (IUS), or other forms of hormonal contraception that have comparable efficacy (failure rate \<1%) * Agree to abstain from breastfeeding during study participation and for at least 12 months following CARCIK-CD19 infusion and until CAR positive viable T cells are no longer present by quantitative polymerase chain reaction (qPCR) on two consecutive tests. 15. Male subjects must: * Practice true abstinence or agree to use a condom during sexual contact with a pregnant female or a female of childbearing potential for 12 months after following CARCIK-CD19 infusion and until CAR positive viable T cells are no longer present by quantitative polymerase chain reaction (qPCR) on two consecutive tests. Exclusion Criteria: 1. Patients with clinically significant active viral, bacterial or fungal infection or any major episode of infection requiring hospitalization or treatment with IV antibiotics (for IV antibiotics this pertains to completion of last course of antibiotic treatment) within 2 weeks prior to CARCIK-CD19 infusion. 2. Patients with an active infection with Hepatitis B. However, patients with a controlled (treated) hepatitis will be allowed if the all the following criteria are met: * Anti-viral therapy for hepatitis B virus (HBV) must be given for at least 1 month prior to time of informed consent; * HBV viral load must be \<2000 IU/mL (104 copies/mL) prior to time of informed consent; and * those on active HBV therapy with viral load \<2000 IU/mL (104 copies/mL) should stay on the same anti-viral therapy throughout study treatment 3. Patients with an active hepatitis C virus (HCV) infection. However, patients with successfully treated chronic HCV infection will be allowed if they show a sustained virologic response at 12 weeks (SVR12) or 24 weeks (SVR24), and if there is a 4-week period between achieving sustained viral response (SVR12 or SVR24) and time of informed consent. 4. Patients with a positive serologic test or a positive molecular PCR test for human immunodeficiency virus (HIV) are eligible if asymptomatic, well controlled by the HAART therapy and no medically significant active infection is present 5. Rapidly progressive disease that in the estimation of the investigator and sponsor could affect compliance with the protocol or interpretation of results 6. Active CNS lymphoma