Blood cell collection could open door to CAR T-Cell therapy for leukemia and lymphoma patients

Copied word for word from the study's registry entry, so the wording is the study team's rather than ours.

* INCLUSION CRITERIA: * Age: \>= 3 and \<= 65 years * Weight \>= 15 kg * Confirmation of cancer diagnosis provided by disease-specific assessment (e.g., flow cytometry, PCR) or H\&E verification. * Disease Status: * Relapsed/refractory cancer that has failed at least one standard regimen and are not in remission at the time of leukapheresis, OR * Previously treated patients without detectable disease at the time of leukapheresis but at high-relapse risk. * Potentially eligible for future NIH-CAR or other adoptive cell therapy based on the following: * Adequate performance status: Patients \> 10 years of age: Karnofsky \>= 50%; Patients \<= 10 years of age: Lansky scale \>= 50% * Adequate organ function: * absolute neutrophil count \>750/mcL\* * platelets \>=30,000/mcL\* * total bilirubin \<=2 X ULN (except in the case of subjects with documented Gilbert s disease \> 3x ULN) AST(SGOT)/ALT(SGPT)\<=20 X institutional upper limit of normal for age and laboratory normal ranges creatinine within age adjusted normal institutional limits (see below) OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for creatinine levels above institutional normal. * Age (Years): \<=5; Maximum Serum Creatine (mg/dL): 0.8 * Age (Years): 5 \< age \<= 10; Maximum Serum Creatine (mg/dL): 1.0 * Age (Years): \>10; Maximum Serum Creatine (mg/dL): 1.2 * Cytopenias deemed to be disease-related and not therapy-related are exempt from this exclusion. * Patients, parents/guardians, legally authorized representative (LAR), or durable power of attorney must be able to give consent and sign the Informed Consent Document. EXCLUSION CRITERIA: * Transfusion refractory thrombocytopenia such that platelet count cannot be adequately supported with transfusions to be at \>=30,000/mcL * Active DIC, bleeding or coagulopathy which cannot be corrected with minimal intervention * Rapidly progressive disease or hyperleukocytosis \>= 50,000 blasts/mcL * Symptomatic, uncontrolled or severe intercurrent illness that would compromise the ability to tolerate CAR or adoptive cell therapy-based toxicity * Subjects must have recovered from the acute side effects of their prior therapy, such that eligibility criteria are met. Cytopenias deemed to be disease-related and not therapyrelated are exempt from this exclusion. * Pregnant or nursing (lactating) individuals, where pregnancy is defined as the state of after conception and until the termination of gestation, confirmed by a positive hCG laboratory test at screening * Active or latent hepatitis B or active hepatitis C, or any uncontrolled infection at screening * Human Immunodeficiency Virus (HIV) infection at screening (The experimental treatments being evaluated depend upon an intact immune system. Patients who are HIV seropositive can have decreased immune competence and thus be less responsive to the experimental treatment and more susceptible to its toxicities) * Any patient that in the opinion of the investigator is not medically stable to undergo the leukapheresis procedure or will not comply with the visit schedules or procedures