CD19.CAR Allogeneic NKT for Patients With Relapsed or Refractory B-Cell Malignancies (ANCHOR)

Earlier, a healthy donor provided blood to make ANCHOR cells in the laboratory. These cells were grown and frozen for later use. To make the ANCHOR cells, the investigators took the donor blood and stimulated it with growth factors to make the NKT cells grow. To get the CD19 antibody, CD28 and IL-15 into the NKT cells, they were infected with a virus, called a retrovirus. This virus cannot grow and infect other cells, but delivered a new genetic message into the ANCHOR cells that provides the instructions for the cells to make the CD19 antibody, CD28 and IL-15. This new genetic message will also help the investigators to find the ANCHOR cells in the blood after they are injected. Because patients will have received cells with a new gene in them, patients will be followed for a total of 15 years to see if there are any long term side effects of gene transfer. Patients will be assigned a dose of ANCHOR cells. This is a dose escalation study. This means that at the beginning, patients will be started on the lowest dose of ANCHOR cells. Once that dose schedule proves safe, the next group of patients will be started at a higher dose. This process will continue until all 4 dose levels are studied. If the side effects are too severe, the dose will be lowered or the infusions will be stopped. In this study, patients will receive treatment with cyclophosphamide and fludarabine. These drugs will decrease the numbers of the patients own immune cells before the ANCHOR cells are infused. The patient will be given an injection of ANCHOR cells into the vein through an IV at the assigned dose. Before receiving the injection, the patient may be given a dose of Benadryl and Tylenol. The injection will take about 20 minutes. The patient will then be monitored in the clinic for up to 2 hours. Certain patients with aggressive lymphomas will need to be admitted to the hospital for the first three days after receiving the cells. Patients will need to stay in Houston for 4 weeks after the ANCHOR cell infusion to monitor them for side effects. Patients will have follow-up visits 3 times per week at weeks 1, 2, 3, 4, and once during week 6; months 3, 6, 9, and 12; twice a year for 4 years and then once a year for the next 10 years - for a total of 15 years). Patients will also have scheduled disease evaluations after the ANCHOR cell infusion (at week 4 and then as clinically needed). The treatment will be given by the Center for Cell and Gene Therapy in Texas Chidren's Hospital or Houston Methodist Hospital. Medical tests before treatment-- Before being treated, the patient will receive a series of standard medical tests: * Physical exam and History * Blood tests to measure blood cells, kidney and liver function * Measurements of tumor by scans and/or bone marrow studies * A urine or serum pregnancy test, when applicable Medical tests during and after treatment-- Patients will receive standard medical tests when getting the infusions and afterwards. The evaluations that will be done at these visits include: * Physical exams and History * Blood tests to measure blood cells, kidney and liver function * Measurements of the tumor by scans at 4-6 weeks, 3 months, 6 months, 9 months and 12 months * If you have disease in the bone marrow, measurements of your tumor by bone marrow studies at 8-12 weeks, 6 months, 9 months and 12 months after the infusion. * To learn more about the way the ANCHOR cells are working and how long they last in the body, extra blood will be drawn. On the day patients receive the cells, blood will be taken before the cells are given and a few hours afterwards. Other blood will be drawn one week after the infusion, 2 weeks, 3 weeks (optional), 4 weeks, and 6 weeks after the infusion, at 3 months, at 6 months, at 9 months, at 1 year, twice a year for 4 years, then yearly for the next 10 years - for a total of 15 years. During the time points listed above, if the ANCHOR cells are found in the patient's blood above a certain amount, an extra 5 mL of blood may need to be collected for additional testing. If the patient has a biopsy of a lymph node, like a repeat tumor or bone marrow study, the investigators may ask to have a piece for research purposes. Patients will receive supportive care for any acute or chronic toxicities, including blood components or antibiotics, and other intervention as appropriate.