Patients meeting specific inclusion and exclusion criteria will be enrolled in two stages, 19 patients in Stage 1 and 36 patients in Stage 2. Stage 2 will enroll if 4 or more patients exhibit a response at Week 8 or later in the study. All enrolled patients will be treated with Fostamatinib Disodium until disease progression. Efficacy will be assessed by tumor measurements using CT and PET (when indicated) scans and physical exam at baseline, and scans and physical exam of all disease-involved areas every 8 weeks until progression. Safety will be assessed by periodic physical exams, clinical laboratory studies, and adverse events. All patients will have a follow-up visit 30 days following last study drug treatment. Blood samples for PK assessment will be obtained from all patients enrolled in Stage 1 at protocol defined intervals.

Up to 61 patients (male and female) meeting the inclusion and exclusion criteria will be enrolled into this trial in two stages. All enrolled patients will be treated with R788 at 200 mg PO bid until disease progression. In the initial stage of the study, a total of 19 patients will be enrolled and treated with Fostamatinib Disodium. Should at least 4 patients exhibit a response at Week 8 or later of the study, the second stage of 36 patients will open to enrollment. Efficacy will be assessed by CT and PET scans (when indicated) and physical exam at baseline, and CT scans and physical exam of all disease-involved areas every 8 weeks until progression. Safety will be assessed by periodic physical exams, clinical laboratory studies, and adverse events. All patients will have a follow-up visit 30 days following last study drug treatment. Blood samples for PK assessment will be obtained from all patients enrolled in Stage 1 at protocol-defined intervals. Patients with accessible tumor tissue will be asked to undergo a biopsy for a fresh tissue sample for assessment of Syk activity in tumor tissue. Archived tissue samples from the initial diagnostic biopsy and the most recent biopsy for lymphoma will be obtained in the event a fresh tumor biopsy cannot be obtained. Patients who have accessible tumor tissue will be asked to consent to a second tumor biopsy at Week 8, to assess the impact of Fostamatinib Disodium treatment on the activity of Syk and its downstream markers. All baseline fresh or archived tumor tissue samples will undergo central pathology review to confirm the diagnosis of TCL.

Inclusion Criteria:

• Patients must give written informed consent to participate in this study by signing an IRB/EC-approved Informed Consent Form (ICF) prior to admission to this study.
• Males and females, 18 years of age or older.
• Patients must have histologically proven T-cell lymphoma (TCL).
• Patients must have documented disease progression after receiving at least one prior therapeutic regimen and must be patients for whom no known curative therapy exists.

Exclusion Criteria:

• Patient has a history of, or a concurrent, clinically significant illness, medical condition or laboratory abnormality that, in the investigator's opinion, could affect the conduct of the study.
• Has a B-cell lymphoma, primary CNS lymphoma, or known lymphomatous involvement of the CNS, or any other NK/T-cell leukemia/lymphoma.
• Has uncontrolled or poorly controlled hypertension.
• Has had recent (within 1 month prior to Day 1) serious surgery or uncontrolled infectious disease.
• Has any concurrent malignancy requiring treatment.
• Has a known positive test for Hepatitis B surface Ag, Hepatitis C, or HIV.
• Has laboratory abnormalities.
• Has difficulty swallowing or malabsorption.
• Has an ECOG performance status > 2.
• Has not recovered from adverse effects related to last prior therapy for lymphoma.
• Has had an allotransplantation within 90 days prior to Day 1 of treatment.
• Has been treated with a CYP3A4 inducer/inhibitor within 3 days prior to Day 1 of treatment or is expected to require treatment with CYP3A4 inducer/inhibitor during the course of the study.
• Has received systemic steroids at a dose greater than the equivalent of 10 mg/day of prednisone within 7 days prior to Day 1 of treatment.
• Has received any other investigational therapy within 5 half-lives of the agent or 2 weeks of Day 1 of treatment, whichever is longer.
• Is a female of childbearing potential unless menopausal, surgically sterile, or willing to use an effective method of birth control, (oral contraceptive, mechanical barrier, long-acting hormonal agent), during the study and for 30 days thereafter.
• Is pregnant or lactating.

This is a small, non-randomized study.