-  INCLUSION CRITERIA:

        Inclusion Criteria

          -  Age greater than or equal to 18 years; no upper age limit.

          -  Patients diagnosed with a leukemia or lymphoma as follows:

               -  Chronic or acute leukemia forms of HTLV-1 associated adult T-cell leukemia;

               -  Peripheral T-cell lymphoma (angioimmunoblastic, hepatosplenic, or not otherwise
                  specified); or,

               -  Cutaneous T-cell lymphoma stage III or IV with circulating monoclonal cells (B1
                  or B2) and/or erythrodermia (T4)

               -  T-cell prolymphocytic leukemia (T-PLL)

        NOTE: Diagnosis must be validated by the Pathology Department, NCI.

        -Patients must have measurable or evaluable disease.

        NOTE: All patients with greater than 10% abnormal CD4+ homogeneous CD3low strongly CD25+
        expressing cells, or greater than 5% S(SqrRoot)(Copyright)zary cells/T-PLL, among the PBMCs
        in the peripheral blood will be deemed to have evaluable disease.

          -  Abnormal T cells must be CD52+ as assessed by flow cytometry or immunohistochemistry.

          -  Patients must have a life expectancy of greater than or equal to 2 months.

          -  Patients must have been refractory or relapsed following front line therapy for ATL;
             those with CTCL or PTCL who have CD30+ disease must have progressed during or after
             treatment with brentuximab vedotin, or are unable to receive treatment due to allergy
             or intolerance.

          -  Patients must have recovered to less than grade 1 or to baseline from toxicity of
             prior chemotherapy or biologic therapy and must not have had major surgery,
             chemotherapy, radiation or biologic therapy within 2 weeks prior to beginning
             treatment. NOTE: Exceptions to this include events not considered to place the subject
             at unacceptable risk of participation in the opinion of the PI (e.g., alopecia).

          -  DLCO/VA and FEV 1.0 > 50% of predicted on pulmonary function tests.

          -  Adequate laboratory parameters, as follows:

               -  Serum creatinine of less than or equal to 1.5 x the upper limit of normal

               -  AST and ALT < 3 x the upper limit of normal

          -  Absolute neutrophil count greater than or equal to 1,500/mm^3 and platelets greater
             than or equal to 100,000/mm^3.

          -  ECOG less than or equal to 1.

          -  Patients must be able to understand and sign an Informed Consent Form.

          -  All patients must use adequate contraception during participation in this trial and
             for 4 months following completing therapy.

        EXCLUSION CRITERIA:

          -  Patients who have received any systemic corticosteroid therapy within 4 weeks prior to
             the start of therapy, or 12 weeks if given to treat graft versus host disease (GVHD),
             with the exception of physiological replacement doses of cortisone acetate or
             equivalent.

          -  Patients who have undergone allogeneic stem cell transplantation and have required
             systemic treatment for GVHD (including but not limited to oral or parenteral
             corticosteroids, ibrutinib, and extracorporeal phototherapy) within the last 12 weeks

          -  Clinical evidence of (parenchymal or meningeal) CNS involvement or metastasis. In
             subjects suspected of having CNS disease, a magnetic resonance imaging (MRI) scan of
             the brain and lumbar puncture should be done to confirm.

          -  Documented HIV, active bacterial infections, active or chronic hepatitis B, hepatitis
             C.

               -  Positive hepatitis B serology indicative of previous immunization (i.e., HBsAb
                  positive and HBcAb negative) or a fully resolved acute hepatitis B infection is
                  not an exclusion criterion.

               -  If hepatitis C antibody test is positive, then the patient must be tested for the
                  presence of HCV by RT-PCR and be HCV RNA negative

        NOTE: HIV-positive patients are excluded from the study. Alemtuzumab may produce a
        different pattern of toxicities in patients with HIV infection; in addition, the depletion
        of T cells produced by alemtuzumab may have adverse effects on HIV-positive individuals.

          -  Concurrent anticancer therapy (including other investigational agents).

          -  History of severe asthma or presently on chronic inhaled corticosteroid medications
             (patients with a history of mild asthma not requiring corticosteroid therapy are
             eligible).

          -  Patients with smoldering and lymphomatous ATL.

          -  Pregnant or nursing patients.

          -  Patients who have previously received alemtuzumab are ineligible. NOTE: Patients with
             relapsed T-PLL who have achieved at least a partial response to prior alemtuzumab are
             eligible.

          -  Uncontrolled intercurrent illness including, but not limited to, ongoing or active
             infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac
             arrhythmia, moderate/severe graft versus host disease, cognitive impairment, active
             substance abuse, or psychiatric illness/social situations that, in the view of the
             Investigator, would preclude safe treatment or the ability to give informed consent
             and limit compliance with study requirements.