Inclusion Criteria:

        Participants must meet all of the following criteria to be included in the study:

          1. Age greater than or equal to 18 years.

          2. Histopathologic diagnosis of CTCL (mycosis fungoides [MF] or Sezary Syndrome [SS]),
             confirmed by skin biopsy, or lymph node, or blood assessment, of current disease.

          3. CD25 assay-positive tumor, defined as detectable CD25 on greater than or equal to 20%
             of total lymphoid infiltrate in biopsied lesions by immunohistochemistry.

          4. CTCL disease stage at study entry as follows, according to ISCL/EORTC (Olsen 2011).

               -  Lead-In Part: Stage IA - IV, except participants with CNS involvement.

               -  Main Study: Stage I - III

          5. History of prior therapies for CTCL: must have had prior therapy, any number of prior
             therapies allowed.

             Topical treatments (except topical chemotherapy) and steroids are not considered as
             prior therapies.

          6. A minimum washout period of 4 weeks after previous CTCL therapy is recommended before
             the first dose of E7777.

             Participants must have recovered from any adverse effects from any previous CTCL
             therapy to Common Terminology Criteria for Adverse Events (CTCAE) Grade <2 before
             starting study drug. A shorter washout may be allowed if participant is experiencing
             progressive disease despite ongoing treatment.

          7. Eastern Cooperative Oncology Group (ECOG) performance status 0, 1, or 2 in the Lead-In
             Part and performance status of 0 or 1 in the Main Study.

          8. Life expectancy greater than or equal to 3 months in the Lead-In Part and greater than
             or equal to 12 months in the Main Study.

          9. Adequate bone marrow reserves as evidenced by:

               -  platelets greater than or equal to 100,000/mm^3 (100 x 10^9/L)

               -  clinically stable hemoglobin greater than or equal to 9 gram per deciliter (g/dL)
                  (90 g/L) and hematocrit greater than or equal to 27% without transfusion support

         10. Normal hepatic function as evidenced by:

               -  bilirubin <= 1.5* upper limit if normal (ULN) and alkaline phosphatase <=3.0*ULN

               -  aspartate aminotransferase (AST) and alanine aminotransferase (ALT) <= 3.0*ULN

               -  albumin >= 3.0 g/dL (30 g/L)

         11. Adequate renal function as evidenced by serum creatinine less than or equal to 1.8
             mg/dL (158 umol/L) or calculated creatinine clearance greater than or equal to 50
             mL/min (per the Cockcroft-Gault formula) with less than 2+ protein or 24- hour urine
             creatinine clearance greater than or equal to 50 mL/minute with 24- hour urine protein
             less than 1gram.

         12. Provide written informed consent prior to any study-specific screening procedures.

         13. Females may not be lactating or pregnant at Screening or Baseline

         14. All females will be considered to be of childbearing potential unless they are
             postmenopausal or have been sterilized surgically

         15. Male participants must have had a successful vasectomy (confirmed azoospermia) or they
             and their female partner must meet the criteria above

        Exclusion Criteria

        Participants who meet any of the following criteria will be excluded from the study:

          1. Prior denileukin diftitox therapy

          2. Use of topical steroids within 14 days of Day 1 of initial therapy is not
             allowed.Topical steroids or systemic low dose steroids of less than or equal to 10
             milligram per day (mg/day) prednisone are allowed in participants with erythroderma
             who have been on corticosteroids for a prolonged period of time and where
             discontinuation may lead to rebound flare in disease. The concomitant steroid
             medication is allowed as long as the type of steroid, route of administration, and
             steroid dose remain the same as what the participant had been receiving for a
             prolonged period of time.

          3. Active malignancy (except for CTCL, definitively treated basal or squamous cell
             carcinoma of the skin, and carcinoma in-situ of the cervix) within the past 24 months.

          4. Serious intercurrent illness

          5. Significant cardiac disease requiring ongoing treatment, including congestive heart
             failure (CHF), severe coronary artery disease (CAD), cardiomyopathy, uncontrolled
             cardiac arrhythmia, unstable angina pectoris, or myocardial infarction (MI)

          6. Significant pulmonary symptoms or disease

          7. History of uncontrolled seizure disorder or active central nervous system disease

          8. Major surgery within 2 weeks of study enrollment

          9. Significant or uncontrolled infections requiring systemic anti-infective therapy

         10. Known human immunodeficiency virus (HIV) infection; known active hepatitis B or
             hepatitis C infection

         11. Females who are pregnant (positive urine test) or breastfeeding

         12. Any history of a medical condition or a concomitant medical condition that, in the
             opinion of the investigator, would compromise the participant's ability to safely
             complete the study.