Treatment to protect the brain will be given inside the spinal using lumbar punctures (spinal taps) with chemotherapy, including methotrexate around day 2 and cytarabine (ara-C) about day 7 of the course. This is done to decrease the risk that the leukemia or lymphoma will develop there. If there is leukemia or lymphoma in the spinal fluid at the time of the first spinal tap, then the treatments will be given more frequently.