Inclusion Criteria:

          -  Patients must have histologically confirmed diffuse large B-cell lymphoma; all
             subtypes of diffuse large B-cell lymphoma are eligible, including high-grade B-cell
             lymphoma and diffuse large B-cell lymphoma (DLBCL) that has transformed from a prior
             indolent B-cell non-Hodgkin lymphoma

          -  Patients must have measurable disease per 2014 Lugano Classification Criteria which is
             defined as at least one nodal lesion measuring > 1.5 cm in greatest diameter or at
             least one extranodal lesion measuring > 1.0 cm in greatest diameter

          -  For phase 2: patients and received at least 2 prior lines of therapy and must have
             previously received, refused, or been deemed ineligible for autologous stem cell
             transplantation

          -  Eastern Cooperative Oncology Group (ECOG) performance status =< 1 (Karnofsky >= 80%)

          -  Absolute neutrophil count >= 1,500/mcL (if neutropenia is related to bone marrow
             involvement with lymphoma, the absolute neutrophil count must be >= 1,000/mcL)

          -  Platelets >= 75,000/mcL (if thrombocytopenia is related to bone marrow involvement
             with lymphoma, the platelet count must be >= 50,000/mcL)

          -  Hemoglobin >= 9 g/dL (if anemia is related to bone marrow involvement with lymphoma,
             the hemoglobin must be >= 8 g/dL)

          -  Total bilirubin =< 1.5 x the institutional upper limit of normal (ULN) or < 3 x the
             ULN for indirect bilirubin in patients with Gilbert's disease

          -  Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =< 2.5 x
             institutional upper limit of normal

          -  Creatinine =< 1.5 x institutional upper limit of normal OR measured or calculated
             creatinine clearance if creatinine > 1.5 x ULN then creatinine clearance >= 40
             mL/min/1.73 m^2 as calculated by Cockcroft and Gault equation

          -  Life expectancy of greater than 3 months

          -  The effects of MK-3475 (pembrolizumab) in combination with KW-0761 (mogamulizumab) on
             the developing human fetus are unknown; for this reason, women of child-bearing
             potential and men must agree to use adequate contraception (hormonal or barrier method
             of birth control; abstinence) prior to study entry and for the duration of study
             participation, and 6 months after completion of MK-3475 (pembrolizumab) in combination
             with KW-0761 (mogamulizumab) administration; should a woman become pregnant or suspect
             she is pregnant while she or her partner is participating in this study, she should
             inform her treating physician immediately; men treated or enrolled on this protocol
             must also agree to use adequate contraception prior to the study, for the duration of
             study participation, and 6 months after completion of MK-3475 (pembrolizumab) in
             combination with KW-0761 (mogamulizumab) administration

          -  Submit adequate archival tissue specimen (25+ unstained slides or 2 tissue blocks)
             from a biopsy performed after progression of disease on most recent therapy OR subject
             is willing to undergo a new core or excisional biopsy to obtain evaluable tumor tissue
             sample for immunohistochemical assessment and sequencing for B2M loss; repeat samples
             may be required if adequate tissue is not provided, however, patients may still be
             considered for enrollment on a case by case basis following consultation with the
             principal investigator (PI)

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

          -  Subjects with prior history of chemotherapy-induced or radiation-induced pulmonary
             toxicity require confirmation of diffuse capacity of the lung for carbon monoxide
             (DLCO) over 60% (adjusted for hemoglobin) by a pulmonary function test prior to study
             enrollment

        Exclusion Criteria:

          -  Patients who have had previous systemic anti-cancer therapy within 3 weeks of
             registration or those who have not recovered from adverse events due to agents
             administered previously

               -  Note: Patients are considered enrolled on the study after protocol registration
                  and not after signing consent

          -  Patients who are receiving any other concurrent investigational agents

          -  Patient is receiving systemic steroid therapy or any other form of immunosuppressive
             therapy within 7 days prior to the first dose of trial treatment; the use of
             physiologic doses of corticosteroids (e.g. prednisone =< 20 mg/d) may be approved
             after consultation with the study PI; topical or inhaled corticosteroids are allowed

          -  Has a known additional malignancy that is progressing or requires active treatment;
             exceptions include basal cell carcinoma of the skin, squamous cell carcinoma of the
             skin that has undergone potentially curative therapy, or in situ cervical cancer

          -  Patients with active cerebral or meningeal 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 evaluation of
             neurologic and other adverse events

          -  History of allergic reactions attributed to compounds of similar chemical or biologic
             composition to MK-3475 (pembrolizumab) or KW-0761 (mogamulizumab)

          -  Subject with active autoimmune disease; subjects with vitiligo, eczema, alopecia, type
             I diabetes mellitus, psoriasis not requiring systemic treatment, or endocrine
             deficiencies (such as hypothyroidism) managed with replacement hormones, including
             physiologic corticosteroid replacement therapy are eligible

          -  Has a history or currently active (non-infectious) pneumonitis that required steroids
             unless prior history of chemotherapy or radiotherapy induced pneumonitis meeting the
             eligibility criteria

          -  Has a history or current evidence of any condition, therapy, or laboratory abnormality
             that might confound the results of the trial, interfere with the patient's
             participation for the full duration of the trial, or is not in the best interest of
             the patient to participate, in the opinion of the treating investigator

          -  Has received prior therapy with an anti-PD-1, anti-PD-L1, anti-PD-L2, or anti-CTLA-4
             antibody (including ipilimumab or any other antibody or drug specifically targeting
             T-cell co-stimulation or checkpoint pathways)

          -  Prior allogeneic stem cell transplant (SCT)

          -  Patients who are planning to receive allogeneic SCT in the near future as preliminary
             reports suggest added toxicity in patients undergoing allogeneic stem cell
             transplantation after having received mogamulizumab

          -  Autologous SCT =< 90 days prior to first dose of study drug

          -  Uncontrolled intercurrent illness including, but not limited to, ongoing or active
             infection, interstitial lung disease or active, non-infectious pneumonitis,
             symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or
             psychiatric illness/social situations that would limit compliance with study
             requirements

          -  Pregnant women are excluded from this study because MK-3475 (pembrolizumab) is an
             agent with 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 MK-3475 (pembrolizumab), breastfeeding should be
             discontinued if the mother is treated with MK-3475 (pembrolizumab); these potential
             risks may also apply to KW-0761 (mogamulizumab)

          -  MK-3475 (pembrolizumab) and KW-0761 (mogamulizumab) may have adverse effects on a
             fetus in utero; furthermore, it is not known if MK-3475 (pembrolizumab) or KW-0761
             (mogamulizumab) has transient adverse effects on the composition of sperm; patients
             are excluded from this study if pregnant or breastfeeding or expecting to conceive or
             father children within the projected duration of the trial, starting with the
             screening visit through 180 days after the last dose of trial treatment

          -  Patients with human immunodeficiency virus (HIV) are excluded if they have a
             detectable viral load, are not on a stable antiretroviral regimen, have a decreased
             CD4+ T-cell count (< 500), or require prophylactic antibiotics for the prevention of
             opportunistic infections

          -  Has a known history of hepatitis B (defined as hepatitis B surface antigen [HBsAg]
             reactive) or known active hepatitis C virus (defined as HCV ribonucleic acid [RNA]
             [qualitative] is detected) infection

               -  Note: No testing for hepatitis B and hepatitis C is required unless mandated by
                  local health authority

          -  Has a known history of active tuberculosis (TB)

          -  Patients with significant cardiac disease (e.g., New York Heart Association [NYHA]
             class III-IV congestive heart failure, unstable angina, recent myocardial infarction
             within the last 6 months, etc.)