Inclusion Criteria:

          -  Participants must have histologically confirmed non-Hodgkin lymphoma and be considered
             ineligible for standard curative therapeutic options, including high dose chemotherapy
             with autologous stem cell rescue.

          -  Participants with the following subtypes of CD52 positive non-Hodgkin lymphoma
             (defined as ≥ 50% positive staining by immunohistochemical staining or flow cytometry
             by local lab) will be considered eligible:

          -  High-grade B-cell lymphoma, with MYC and BCL2 and/or BCL6 rearrangements (DHL)

          -  DLBCL or high-grade B-cell lymphoma NOS or B-cell lymphoma unclassifiable with
             features intermediate between Burkitt lymphoma and diffuse large B-cell lymphoma with
             MYC and BCL2 protein over-expression by immunohistochemical (IHC) staining as defined
             by MYC expression in ≥ 40% of cells and BCL2 positivity ≥ 50% (DOL)

          -  Transformed lymphoma with MYC rearrangement by FISH or over-expression by IHC, as
             above

          -  CD52 positive mature T-cell lymphoproliferative disorder

          -  There is no limit to the prior number of chemotherapy regimens. Patients with prior
             autologous or allogeneic stem cell transplantation, as well as prior therapy with
             cyclophosphamide or alemtuzumab, are eligible.

          -  Age ≥ 18 and ≤75

          -  ECOG performance status ≤2 (Karnofsky ≥60%, see Appendix A)

          -  Participants must have normal organ and marrow function as defined by peripheral blood
             values below:

               -  leukocytes ≥1,000/mcL

               -  absolute neutrophil count ≥500/mcL

               -  platelets ≥25,000/mcL

               -  total bilirubin ≤ 2 × institutional upper limit of normal (ULN) unless related to
                  Gilbert's disease

               -  AST(SGOT)/ALT(SGPT) ≤ 3 × institutional ULN

               -  creatinine clearance < 1.5 x institutional ULN

          -  Ability to understand and the willingness to sign a written informed consent document.

        Exclusion Criteria:

          -  Participants who have had chemotherapy or radiotherapy within 1 weeks (4 weeks for
             nitrosoureas or mitomycin C) prior to entering the study or those who have not
             recovered from adverse events due to agents administered more than 4 weeks earlier.

          -  Participants who are receiving any other investigational agents for their lymphoma.

          -  Participants receiving corticosteroids within the past 1 week.

          -  Participants with known active CNS involvement by lymphoma should be excluded from
             this clinical trial because of their poor prognosis and because they often develop
             progressive neurologic dysfunction that would confound the evaluation of neurologic
             and other adverse events.

          -  History of allergic reactions attributed to cyclophosphamide or alemtuzumab

          -  Uncontrolled intercurrent illness including, but not limited to, ongoing or active
             infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac
             arrhythmia, uncontrolled hematuria related to bladder injury or psychiatric
             illness/social situations that could limit compliance with study requirements.

          -  Pregnant women are excluded from this study because cyclophosphamide and alemtuzumab
             at these doses have the potential for teratogenic or abortifacient effects. Because
             there is an unknown but potential risk for adverse events in nursing infants secondary
             to treatment of the mother with these agents, breastfeeding should be discontinued.
             Negative serum pregnancy test will be required for women of childbearing potential.

          -  HIV-positive participants on combination antiretroviral therapy are ineligible because
             of the increased risk of lethal infections when treated with marrow-suppressive
             therapy.