Umbilical & Cord Blood (CB) Derived CAR-Engineered NK Cells for B Lymphoid Malignancies

Inclusion Criteria: 1. Patients with history of CD 19 positive B-lymphoid malignancies (ALL, CLL, NHL) who have received at least 2 lines of standard chemoimmunotherapy or targeted therapy and have persistent disease. 2. Patients with ALL, CLL, NHL with relapsed disease following standard therapy or a stem cell transplant. 3. Patients at least 3 weeks from last cytotoxic chemotherapy at the time of starting lymphodepleting chemotherapy. Patients may continue tyrosine kinase inhibitors or other targeted therapies until at least two weeks prior to administration of lymphodepleting chemotherapy. 4. Karnofsky/Lansky Performance Scale \> 70. 5. Adequate organ function: a. Renal: Creatinine clearance (as estimated by Cockcroft Gault) \>/= 60 cc/min. b. 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. c. Cardiac: Cardiac ejection fraction \>/= 50%, no evidence of pericardial effusion as determined by an ECHO or MUGA, and no clinically significant ECG findings. d. Pulmonary: No clinically significant pleural effusion, baseline oxygen saturation \> 92% on room air. 6. Able to provide written informed consent. 7. 7-80 years of age. 8. All participants who are able to have children must practice effective birth control while on study. Acceptable forms of birth control for female patients include: hormonal birth control, intrauterine device, diaphragm with spermicide, condom with spermicide, or abstinence, for the length of the study. If the participant is a female and becomes pregnant or suspects pregnancy, she must immediately notify her doctor. If the participant becomes pregnant during this study, she will be taken off this study. Men who are able to have children must use effective birth control while on the study. If the male participant fathers a child or suspects that he has fathered a child while on the study, he must immediately notify his doctor. 9. Signed consent to long-term follow-up protocol PA17-0483. Exclusion Criteria: 1. Positive beta HCG in female of child-bearing potential defined as not postmenopausal for 24 months or no previous surgical sterilization or lactating females. 2. Known positive serology for HIV. 3. Presence of Grade 3 or greater toxicity from the previous treatment. 4. Presence of fungal, bacterial, viral, or other infection requiring IV antimicrobials for management. Note: Simple UTI and uncomplicated bacterial pharyngitis are permitted if responding to active treatment. 5. Presence of active neurological disorder(s). 6. Concomitant use of other investigational agents.