Inclusion Criteria:

   - Patients must have a diagnosis of CLL/SLL or B-cell prolymphocytic leukemia, as
   defined by the World Health Organization (WHO)

   - During dose escalation, patients must have received at least one prior therapy, need
   additional cytoreduction, and meet criteria for relapsed or refractory disease;
   relapsed disease is defined as a patient who previously achieved a CR or a PR, but
   after a period of six or more months demonstrates evidence of disease progression;
   refractory disease is defined as progression within six months of the last
   anti-leukemic therapy, or any response less than a CR or PR; patients who are
   previously untreated, and do not wish to receive chemotherapy or immunotherapy, are
   eligible for the dose expansion portion of the study

   - Patients may have not received treatment for 28 days before the first day of the study
   protocol (dose escalation only)

   - Estimated life expectancy greater than two months

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

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

   - Patients must have acceptable organ and marrow function, which should be present
   independent of growth factor or transfusion support for at least 7 days prior to first
   dose of study drug, with the exception of pegylated G-CSF (pegfilgrastim) and
   darbopoeitin which require a 14-day period between dosing and first dose of study drug

   - Absolute neutrophil count (ANC) >= 750 cells/uL (0.75 x 10^9/L)

   - Platelets >= 50,000 cells/uL (50 x 10^9/L)

   - Hemoglobin > 8 mg/dL

   - Total bilirubin =< 1.5 x upper limit of normal (ULN) unless Gilbert's syndrome or
   disease infiltration of the liver is present

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

   - Creatinine < 2.0 x ULN or creatinine clearance (estimated [est.] glomerular filtration
   rate [GFR] [Cockcroft-Gault]) >= 30 mL/min

   - Prothrombin time (PT)/international normalized ratio (INR) < 1.5 x ULN and partial
   thromboplastin time (PTT)/activated partial thromboplastin time (aPTT) < 1.5 x ULN

   - The effects of ibrutinib on the developing human fetus are unknown; lenalidomide is
   likely to be teratogenic; therefore, females of childbearing potential (FCBP) must
   have a negative pregnancy test (sensitivity of at least 25 mIU/mL) performed once
   before ibrutinib and a total of two negative tests before initiating lenalidomide; a
   FCBP is a female who: 1) has achieved menarche at some point; 2) has not undergone a
   hysterectomy or bilateral oophorectomy; or 3) has not been naturally postmenopausal
   (amenorrhea following cancer therapy does not rule out childbearing potential) for at
   least 24 consecutive months (i.e., has had menses at any time in the preceding 24
   consecutive months); the pre-ibrutinib pregnancy test will be initiated at enrollment;
   the first pre- lenalidomide test will be performed within 10-14 days of starting
   lenalidomide (cycle 0, day 15), and the second pre-lenalidomide test (3rd total test)
   will be within 24 hours of the first dose of lenalidomide; the patient may not receive
   lenalidomide until the study doctor has verified that the results of these pregnancy
   tests are negative; pregnancy tests (if applicable) are then to be conducted weekly
   during the first month, and monthly thereafter in women with a regular menstrual
   cycle, as well as at study discontinuation, and at day 28 following study
   discontinuation; if menstrual cycles are irregular, pregnancy testing will be
   conducted weekly for the first month, and then every 14 days while on the study, at
   study discontinuation, and at days 14 and 28 following study drug discontinuation;
   pregnancy testing and counseling are to be performed if a patient misses her period or
   if there is any abnormality in menstrual bleeding; should a woman become pregnant or
   suspect she is pregnant while she is participating in this study, she should inform
   her treating physician immediately; further, FCBP must either commit to continued
   abstinence from heterosexual intercourse or begin TWO acceptable methods of birth
   control: one highly effective method and one additional effective method AT THE SAME
   TIME, at least 28 days before starting lenalidomide; FCBP must also agree to ongoing
   pregnancy testing; men must agree to use a latex condom during sexual contact with a
   FCBP, even if they have had a successful vasectomy; male and female patients must
   agree to use highly effective methods of birth control (e.g. condoms, implants,
   injectables, combined oral contraceptives, some intrauterine devices [IUDs], complete
   sexual abstinence, or sterilized partner) during the period of therapy and for 90 days
   after the last dose of study drug; all patients must be counseled by a trained
   counselor every 28 days about pregnancy precautions and risks of fetal exposure

Exclusion Criteria:

   - Prior therapy with Bruton's tyrosine kinase (BTK) inhibitor

   - Concurrent treatment with other investigational or anti-neoplastic agents

   - Patients requiring daily corticosteroids at a prednisone equivalent of > 20 mg daily
   should not be enrolled; if corticosteroids can be discontinued (or reduced to < 20 mg
   per day of prednisone or equivalent), the discontinuation or dose reduction should be
   done at least 7 days prior to first dose

   - Chemotherapy =< 21 days prior to first administration of study treatment and/or
   monoclonal antibody =< 6 weeks prior to first administration of study treatment;
   immunotherapy, radiotherapy or experimental therapy within 28 days of first day of
   study drug dosing, or within six weeks of first day of study drug dosing in the event
   that nitrosoureas or mitomycin were used; concurrent systemic immunosuppressant
   therapy other than corticosteroids (e.g. cyclosporine A, tacrolimus, etc) must be
   discontinued within 28 days of the first dose of study drug

   - Currently active clinically significant cardiovascular disease such as uncontrolled
   arrhythmia, congestive heart failure, or any class 3 or 4 congestive heart failure as
   defined by the New York Heart Association Functional Classification, or history of
   myocardial infarction, unstable angina or acute coronary syndrome within 6 months
   prior to on-study registration

   - Uncontrolled psychiatric illness that would limit compliance with study requirements

   - Central nervous system disease involvement; these patients 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 prior malignancy, with the exception of the following:

      - Malignancy treated with curative intent and with no evidence of active disease
      present for more than 3 years prior to screening, and felt to be at low risk for
      recurrence by treating physician

      - Adequately treated non-melanomatous skin cancer or lentigo maligna melanoma
      without current evidence of disease

      - Adequately treated cervical carcinoma in situ without current evidence of disease

   - Serologic status reflecting active hepatitis B or C infection; patients that are
   hepatitis B core antibody, hepatitis B surface antigen (HBsAg) or hepatitis C antibody
   must have a negative polymerase chain reaction (PCR) prior to enrollment; PCR positive
   patients will be excluded

   - Active infection at initiation of study; recent infections requiring systemic
   treatment need to have completed therapy > 14 days before the first dose of study drug

   - Major surgery within 4 weeks or minor surgery within 7 days of the first day of study
   drug dosing

   - Unable to swallow capsules or disease significantly affecting gastrointestinal
   function or resection of the stomach or small bowel, or symptomatic inflammatory bowel
   disease or ulcerative colitis or partial or complete bowel obstruction

   - Prior allogeneic stem cell transplantation

   - Active, uncontrolled autoimmune hemolytic anemia or idiopathic thrombocytopenic
   purpura (ITP)

   - Presence of transfusion-dependent thrombocytopenia or a history of bleeding disorders
   or clinical conditions (e.g. gastrointestinal [GI] bleeding or constitutional
   disorders) that may increase risk of life-threatening bleeding when thrombocytopenic

   - History of stroke or intracranial hemorrhage within 6 months prior to enrollment

   - History of allergic reactions attributed to compounds of similar chemical or biologic
   composition to ibrutinib or lenalidomide

   - Patients who received a strong cytochrome P450 (CYP) 3A inhibitor within 7 days prior
   to the first dose of ibrutinib or patients who require continuous treatment with a
   strong CYP3A inhibitor

   - Requires or is receiving anticoagulation with warfarin or equivalent vitamin K
   antagonists (e.g.: phenprocoumon) within 28 days of the first dose of study drug

   - Pregnant women are excluded from this study because ibrutinib and lenalidomide 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 ibrutinib and lenalidomide, breastfeeding should be discontinued if the
   mother is treated with either agent, and for 30 days after discontinuation of therapy

   - Current life-threatening illness, medical condition, or organ system dysfunction
   which, in the investigator's opinion, could compromise the patient's safety, or put
   the study at risk

   - Human immunodeficiency virus (HIV)-positive patients with cluster of differentiation 4
   (CD4) counts less than the lower limit of institutional normal

   - HIV-positive patients requiring antivirals which are cytochrome P450 (CYP) interactive
   with the investigational agents (CYP3A4 strong inducers and inhibitors)

   - Other laboratory abnormalities that, in the opinion of the investigator, would
   compromise the patient's safety or interfere with data interpretation

   - Vaccinated with live, attenuated vaccines within 4 weeks of first dose of study drug

   - Unresolved toxicities from prior anti-cancer therapy, defined as having not resolved
   to Common Terminology Criteria for Adverse Event (CTCAE, version 5), grade =< 1, or to
   the levels dictated in the inclusion/exclusion criteria with the exception of alopecia

   - Known bleeding disorders (e.g., von Willebrand's disease) or hemophilia

   - Unwilling or unable to participate in all required study evaluations and procedures

   - Currently active, clinically significant hepatic impairment (>= moderate hepatic
   impairment according to the National Cancer Institute (NCI)/Child Pugh classification)