Administration of TAA-Specific CTLs; Hodgkin or Non-Hodgkin Lymphoma; TACTAL

The patient will give blood to make TAA-specific cytotoxic T cells in the lab. These cells will be grown and frozen. If the TAA-specific cytotoxic T cells can be made, the time from collection of the blood to manufacture of T cells for administration to the patient is about 1 to 2 months. There are 4 stages of this study: an antigen-escalation phase, a dose-escalation stage, aza stage and pediatric patients stage. The antigen-escalation phase will be first. Patients will receive TAA-specific T cells targeting first 1 and then 2 TAAs. Once this schedule proves safe, the next group of patients will receive TAA-specific T cells targeting first 2 and then 3 TAAs. This process will continue until all 4 levels are studied. This means that the final cohort of patients will receive TAA-specific T cells targeting first 4 and then 5 TAAs. If the side-effects are too severe, the number of TAAs being targeted will be lowered or the T cell injections will be stopped. Each patient will receive 2 infusions at the same dose 28 days apart After the antigen-escalation phase, the dose-escalation phase will begin. Patients will be started on the lowest dose (1 of 3 different levels) of T 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 3 dose levels are studied. If the side-effects are too severe, the dose will be lowered or the T cell injections will be stopped. Each patient will receive 2 infusions at the same dose 14 days apart After the dose escalation stage, adult patients will be enrolled on the aza stage where they will receive the drug aza followed by two infusions of T cells on dose level 2. Patients will be given 3 cycles of aza (administered daily through a vein for 5 days, every 28 days) followed by 2 doses of multiTAA-specific T cells administered 14 days apart. Before the patient is given the aza they will be given a drug to help prevent nausea and vomiting. On the pediatric stage, pediatric patients will receive 2 infusions of T cells on dose level 2. The T cells will be given 14 days apart. The cells will be injected by IV over 10 minutes. The patients may be pre-treated with acetaminophen (Tylenol) and diphenhydramine (Benadryl). Acetaminophen (Tylenol) and diphenhydramine (Benadryl) are given to prevent a possible allergic reaction to the T cell administration. If after the second infusion there is a reduction in the size of the patient's lymphoma on CT or MRI scan as assessed by a radiologist, the patient can receive up to six (6) additional doses of the T cells at monthly intervals if they wish. All of the treatments will be given by the Center for Cell and Gene Therapy at Houston Methodist Hospital or Texas Children's Hospital. In between the first and second T cell infusions and for 6 weeks after the last infusion, the patient should not receive any other anti-cancer treatments such as radiation therapy or chemotherapy. If the patient does receive any other therapies in-between the first and second infusion of T cells, they will be taken off treatment and will not be able to receive the second infusion of T cells. MEDICAL TESTS BEFORE TREATMENT * Physical exam. * Blood tests to measure blood cells, kidney and liver function. * Measurements of your tumor by routine imaging studies. We will use the imaging study that was used before to follow your tumor: CT, MRI, or PET. * Pregnancy test if you are a female who can have children. MEDICAL TESTS AFTER TREATMENT \- Imaging study 6 weeks after the 2nd TAA-CTL infusion. To learn more about the way the T cells are working in the patient's body, an extra 20-40 mL (4-8 teaspoons) of blood will be taken before each cycle of aza (if applicable), 2 weeks after each cycle of aza (if applicable), before each T-cell infusion, and at Weeks 1, 2, 4 and 6. One additional blood sample might be drawn 3 to 4 days post the T-cell infusion; this is optional. Afterwards, blood will be collected at 3, 6, 9 and 12 months after the last infusion. The blood may be drawn from a central line at the time of the patient's regular blood tests. Investigators will use this blood to see how long the T cells last,and to look at the immune response to the patient's cancer. Study Duration: Patients will be on active study participation for approximately one year. Patients who receive additional doses of the T cells as described above will be actively followed until 1 year after their last dose of T cells. Investigators will then remain in contact with patients once a year for up to 4 additional years (total of 5 years follow-up) in order to evaluate disease response long-term.