(TAA)-Specific Cytotoxic T-Lymphocytes to Pediatric Patients With Lymphomas (pediTACTAL).

First, patients provide blood for us to make TAA-specific cytotoxic T cells in the lab. The amount of blood to be drawn will be less based on the child's weight per blood draw (3 mL/kg). Under certain conditions related to the patient's health, investigators may need to collect the blood using a process called apheresis. Apheresis is the process where blood is passed through a machine that separates out the components of the patient's blood that is needed. The remainder of the patient's blood is then returned to the patient's body. 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. The cells will then be injected by IV into the patient over 10 minutes. The patient 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. Initially, two doses of T cells will be given two weeks apart. The patient's lymphoma will be assessed before the infusion (pre-infusion) and then 6 weeks after the second infusion. If after the patient's second infusion he/she has not relapsed or experienced a side effect which would prevent him/her from receiving any more cells, he/she can receive up to six (6) additional doses if they wish. The T cells would then be given at 6-8 week intervals. In between the first and second T cell infusions and for 6 weeks after the last infusion, investigators ask that the patient 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. All of the treatments will be given by the Center for Cell and Gene Therapy at Texas Children 's Hospital. MEDICAL TESTS BEFORE TREATMENT Before being treated,the patient will receive a series of standard medical tests: * Physical exam. * Blood tests to measure blood cells, kidney and liver function. * Measurements by routine imaging studies to confirm the patient is in remission. Investigators will use the imaging study that was used before to follow the patient's tumor: CT, MRI, or PET. * Pregnancy test if the patient is a female who can have children. MEDICAL TESTS AFTER TREATMENT \- Imaging study 8 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 or 3ml/kg of body weight of blood (whichever is less) will be taken before the infusion, and at weeks 2, 4 and 8. Afterwards, blood will be collected at 3, 6, 9 and 12 months after the last infusion. The blood may be drawn from the patient's central line at the time of his or her regular blood tests. Investigators will use this blood to see how long the T cells last, and to look at the patient's immune response to their cancer. If the patient receives additional doses of T cells this blood will also be collected before each infusion and 1, 2, 4, and 6 weeks post each infusion. The maximum amount of blood that may be drawn over the course of the study is 156 to 312 teaspoon. Investigators may request a sample of a previous tumor biopsy the patient has had or from a tumor biopsy performed at any time while the patient is on this study. The sample will be used for research purposes related to this study. In the event of death, investigators will request permission to perform an autopsy to learn more about the effects of the treatment on the patient's disease. STUDY DURATION The patient's active participation in this study will last for approximately one 1 year. If they receive additional doses of the T cells as described above, their active participation will last until one 1 year after their last dose of T cells. Investigators will then contact them once a year for up to 4 additional years (total of 5 years follow-up) in order to evaluate their disease response long-term.