Inclusion Criteria:

          -  PHASE I: Histologically confirmed B-cell NHL with any of the following subtypes:
             DLBCL, mantle cell lymphoma (MCL), FL, marginal zone lymphoma (MZL) and
             lymphoplasmacytic lymphoma/Waldenstrom's macroglobulinemia (LL/WM), Burkitt's lymphoma
             (BL); patients with histological transformation to DLBCL from indolent lymphoma,
             primary mediastinal lymphoma and grey zone lymphoma are eligible

          -  PHASE I: Histologically confirmed classical or lymphocyte predominant Hodgkin's
             disease that is relapsed or refractory after at least one prior chemotherapy

          -  PHASE I: Patients must have received at least one prior therapy; prior autologous stem
             cell transplant is permitted; patients with DLBCL who have not had prior high-dose
             therapy (HDT)/autologous stem cell transplant (ASCT) must be ineligible for
             transplant; prior lenalidomide is not permitted if patients have progressed on therapy

          -  PHASE IB DOSE EXPANSION: Histologically confirmed classical or lymphocyte predominant
             Hodgkin's disease

          -  PHASE IB DOSE EXPANSION: Patients must have received at least one prior therapy; prior
             autologous stem cell transplant is permitted; patients who have not had prior HDT/ASCT
             must be ineligible for transplant; prior lenalidomide is not permitted if patients
             have progressed on therapy

          -  PHASE II: Histologically confirmed B-cell NHL:

               -  Cohort 1: with only de novo DLBCL or transformed indolent Non-Hodgkin's lymphoma
                  (excludes Richter's syndrome).

               -  Cohort 2: with only FL of grade 1, 2 or 3a

          -  PHASE II: Patients must have received at least one prior therapy (in patients with
             transformed DLBCL must have received at least one prior therapy; prior autologous stem
             cell transplant is permitted; patients with DLBCL who have not had prior HDT/ASCT must
             be ineligible for transplant; prior lenalidomide is not permitted if patients have
             progressed on therapy

          -  Be willing and able to provide written informed consent/assent for the trial

          -  Have evaluable disease

          -  Eastern Cooperative Oncology Group (ECOG) performance status of 0-2

          -  Absolute neutrophil count (ANC) >= 1,500 /mcL

          -  Platelets >= 100,000 /mcL in the absence of transfusion support within 7 days of
             determining eligibility

          -  Hemoglobin >= 8 g/dL

          -  Serum creatinine =< 1.5 X upper limit of normal (ULN) OR measured or calculated
             creatinine clearance (glomerular filtration rate [GFR] can also be used in place of
             creatinine or creatinine clearance [CrCl]) >= 40 mL/min creatinine clearance

          -  Serum total bilirubin =< 1.5 X ULN OR except subjects with Gilbert syndrome, who can
             have total bilirubin < 3.0 mg/dL

          -  Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase [SGOT]) and
             alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 3.0 X
             ULN

          -  Female subject of childbearing potential should have a negative urine or serum
             pregnancy at screening and within 24 hours prior to receiving the first dose of study
             medication; if the urine test is positive or cannot be confirmed as negative, a serum
             pregnancy test will be required

          -  Female subjects of childbearing potential should be willing to use 2 methods of birth
             control or be surgically sterile, or abstain from heterosexual activity for the course
             of the study through 120 days after the last dose of study medication; subjects should
             agree to ongoing pregnancy testing during the course of the study and after the end of
             study therapy; female subjects of childbearing potential are those who have not been
             surgically sterilized or have not been free from menses for > 1 year

          -  Male subjects should agree to use an adequate method of contraception starting with
             the first dose of study therapy through 120 days after the last dose of study therapy;
             males must refrain from donating sperm during study participation and for 120 days
             after the last dose of study medication

          -  Willing and able to receive adequate prophylaxis and/or therapy for thromboembolic
             events

          -  Be willing and able to understand and give written informed consent and comply with
             all study related procedures

        Exclusion Criteria:

          -  Is currently participating and receiving study therapy or has participated in a study
             of an investigational agent and received study therapy or used an investigational
             device within 3 weeks of the first dose of treatment

          -  Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any
             other form of immunosuppressive therapy within 7 days prior to the first dose of trial
             treatment; subjects may use topical or inhaled corticosteroids or low-dose steroids
             (=< 20 mg of prednisone or equivalent per day) as therapy for comorbid conditions;
             during study participation, subjects may receive systemic or enteric corticosteroids
             as needed for treatment-emergent comorbid conditions

          -  Has a known history of active TB (bacillus tuberculosis)

          -  Hypersensitivity to nivolumab or lenalidomide or any of their excipients

          -  Has had a prior anti-cancer monoclonal antibody (mAb) within 2 weeks prior to study
             day 1 or who has not recovered (i.e., =< grade 1 or at baseline) from adverse events
             due to agents administered more than 4 weeks earlier

          -  Has had prior chemotherapy or radiation therapy within 2 weeks prior to study day 1 or
             who has not recovered (i.e., =< grade 1 or at baseline) from adverse events due to a
             previously administered agent

               -  Note: subjects with =< grade 2 neuropathy are an exception to this criterion and
                  may qualify for the study

               -  Note: if subject received major surgery, they must have recovered adequately from
                  the toxicity and/or complications from the intervention prior to starting
                  therapy; patients must be 4 weeks out from major procedures

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

          -  Has known active central nervous system (CNS) lymphoma

          -  Has active autoimmune disease that has required systemic treatment in the past 2 years
             (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive
             drugs); replacement therapy (thyroxine, insulin, or physiologic corticosteroid
             replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a
             form of systemic treatment; conditions expected to not recur in the absence of an
             external trigger

          -  Has an active infection requiring intravenous systemic therapy

          -  Is unable to swallow capsules or malabsorption syndrome, disease or condition
             significantly affecting gastrointestinal function

          -  Clinically significant cardiovascular disease with uncontrolled arrhythmia, New York
             Association class 3 or 4 congestive heart failure, history of myocardial infarction
             within 6 months, or prolonged corrected QT (QTc) > 500 msec

          -  Is pregnant or breastfeeding, or expecting to conceive or father children within the
             projected duration of the trial, starting with the pre-screening or screening visit
             through 120 days after the last dose of trial treatment

          -  Has progressed on prior therapy with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent

          -  Has progressed on prior therapy with lenalidomide

          -  Has a known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies)

          -  Has known active hepatitis B (e.g., hepatitis B surface antigen [HBsAg] reactive) or
             hepatitis C (e.g., hepatitis C virus [HCV] ribonucleic acid [RNA] [qualitative] is
             detected)

          -  Has a history of deep venous thrombosis/embolism, threatening thromboembolism or known
             thrombophilia or are at a high risk for a thromboembolic event in the opinion of the
             investigator and who are not willing/able to take venous thromboembolic event
             prophylaxis during the entire treatment period

          -  Has a history of prior allogeneic hematopoietic cell transplant with a history of
             prior Graft Versus Host Disease