Metabolically Fit CD19 CAR T-cell Therapy With CD34 Selection in Patients With CD19+ Relapsed/Refractory NHL, CLL/SLL

This study is testing a new type of immune cell therapy (CAR T-cells) for people with certain types of B-cell blood cancers that have come back or stopped responding to treatment. The CAR T-cells are specially engineered to target a protein called CD19, found on the surface of these cancer cells. **You may be eligible if...** - You have a CD19-positive B-cell lymphoma (including DLBCL, follicular lymphoma, mantle cell lymphoma, and others), CLL, or SLL that has relapsed or is not responding to treatment - You have received prior treatment for your cancer - You are in reasonably good health as measured by standard performance scores - Your heart, liver, kidney, and blood counts meet the required levels **You may NOT be eligible if...** - Your cancer does not express the CD19 protein - You have active, uncontrolled infection or autoimmune disease - You have significant heart, lung, liver, or kidney problems - You have had a prior CAR T-cell therapy recently or certain other immune therapies - You are pregnant or breastfeeding Talk to your doctor to see if this trial is right for you.