⁃ Stratum I/II (Adults):

• Confirmed CD19+ ALL, CLL, DLBCL, FL or MCL in patients ≥ 18 years

• ALL (Ph+ and Ph-): Confirmed CD19+ ALL by cytology and flow cytometry (FACS) AND

• Relapsed or refractory disease (including molecular relapse with minimal residual disease (MRD) levels \> 10\^-3 at two occasions \> 2 weeks apart) with confirmed CD19 expression on malignant cells in relapse

‣ Any relapse after allogeneic stem cell transplantation (alloSCT) (≥ 6 months from alloSCT at time of CAR T cell infusion) OR

⁃ Any relapse failing to achieve an MRD level of \< 10\^-3 after ≥ 2 lines of treatment OR

⁃ Primary refractory as defined by not achieving a complete remission (CR) after ≥ 2 lines of treatment

• CLL/NHL: Confirmed CD19+ CLL/NHL (including CLL, DLBCL, FL or MCL) with

‣ CLL in need of treatment with:

• Early relapse (within 2 years) after end of chemoimmunotherapy or chemoimmunotherapy refractoriness plus failure or intolerance of both Bruton's tyrosine kinase Inhibitor (BTKi) and B-cell lymphoma 2 inhibitors (BCL-2i) OR

∙ Relapse after alloSCT, ineligible for or refractory to standard interventions (donor lymphocyte infusions (DLI), CD20 antibodies, chemoimmunotherapy)

⁃ DLBCL with:

• Refractoriness to a 2nd or later line of chemoimmunotherapy OR

∙ Relapse after autologous stem cell transplantation (autoSCT) plus ineligibility for alloSCT (including refractoriness to one line of salvage chemoimmunotherapy) OR

∙ Relapse after alloSCT

⁃ FL in need of treatment with:

• Relapse \<2 years after chemoimmunotherapy AND ineligibility for or failure of autologous stem cell transplantation (autoSCT) AND ineligibility for or failure of idelalisib OR

∙ Relapse after alloSCT, ineligible for or refractory to standard interventions (DLI, CD20 antibodies, chemoimmunotherapy)

⁃ MCL with:

• Relapse after standard first-line therapy AND ineligibility for or failure to BTKi salvage therapy OR

∙ Relapse after alloSCT AND ineligibility for or failure to BTKi salvage therapy

• Measurable disease/MRD at time of enrollment

• Life expectancy ≥ 12 weeks

• Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 at the time of screening

• Adequate organ function:

‣ Renal function defined as: serum creatinine of ≤ 2 x ULN or estimated glomerular filtration rate (eGFR) ≥ 30 mL/min/1.73 m\^2

⁃ Liver function defined as:

⁃ ALT ≤ 5 times the ULN for the respective age

⁃ Bilirubin ≤ 2.0 mg/dl with the exception of patients with hyperbilirubinemia explained by Gilbert-Meulengracht syndrome (may be included if total bilirubin is ≤ 3.0 x ULN and direct bilirubin ≤ 1.5 x ULN) or extrahepatic disease (e.g. chronic hemolytic anemia)

⁃ minimum level of pulmonary reserve defined as ≤ grade 1 dyspnea and pulse oxygenation \> 90% on room air

⁃ Hemodynamic stability and left ventricular ejection fraction (LVEF) ≥ 40% as confirmed by echocardiogram

⁃ Absolute neutrophil count (ANC) ≥ 500/mm3

⁃ Absolute lymphocyte count (ALC) ≥ 100/mm3

• Women of child-bearing potential (defined as all women physiologically capable of becoming pregnant) and all male participants must agree to use highly effective methods of contraception for one year following CD19.CAR T cell therapy

• Ability to understand the nature of the trial and the trial related procedures

• Written informed consent must be obtained prior to any screening procedures

⁃ Stratum III (Children and Adolescents with ALL):

• Age of \> 3 years until \< 18 years at the time of screening

• CD19+ ALL (Ph+ and Ph-) confirmed by cytology and flow cytometry (FACS) AND

• Relapsed or refractory disease (including molecular relapse with polymerase chain reaction (PCR) MRD \> 10\^-3 at two occasions \> 2 weeks apart) with confirmed CD19 expression on malignant cells in relapse

‣ Any relapse after alloSCT (≥ 6 months from alloSCT at time of CAR T cell infusion) OR

⁃ Any relapse failing to achieve an MRD level of \< 10\^-3 after ≥ 2 lines of treatment OR

⁃ Primary refractory as defined by not achieving a CR after ≥ 2 lines of treatment

• Measurable disease/MRD at time of enrollment

• Life expectancy ≥ 12 weeks

• ECOG performance status ≤ 2 (age ≥ 16 years) or Lansky performance status ≥ 50 (age \< 16 years) at the time of screening

• Adequate organ function:

‣ Renal function defined as serum creatinine-clearance ≥ 30 mL/min/1.73 m\^2

⁃ Liver function defined as:

⁃ ALT ≤ 5 times the ULN for the respective age

⁃ Bilirubin ≤ 2.0 mg/dl with the exception of patients with hyperbilirubinemia explained by Gilbert-Meulengracht syndrome or extrahepatic disease (e.g. chronic hemolytic anemia)

⁃ minimum level of pulmonary reserve defined as ≤ grade 1 dyspnea and pulse oxygenation \> 90% on room air

⁃ Hemodynamic stability and LVEF ≥ 40% or shortening fraction \> 29% as confirmed by echocardiogram

⁃ ANC) ≥ 500/mm3

⁃ ALC ≥ 100/mm3

• Women of child-bearing potential (defined as all women physiologically capable of becoming pregnant) and postpubertal male participants must agree to use highly effective methods of contraception for one year following CD19.CAR T cell therapy

• Written informed consent of the study patient and/or the legal representative must be obtained prior to any screening procedures