PARTICIPANTS NOT ON THE HODGKIN LYMPHOMA EXPANSION COHORT: Creatinine < 1.5 UNL or creatinine clearance (CrCl) > 50 ml/min, within 2 weeks prior to enrollment Serum creatinine =< 1.5 x upper limit of normal (ULN) or serum creatinine clearance (CrCl) >= 40 ml/min, obtained within 4 weeks prior to randomization Serum creatinine ? 1.5 × upper limit of normal (ULN) or creatinine clearance (CrCl) ? 40 mL/min/1.73 m2 Creatinine clearance (CrCl) >= 60 mL/min Patients with severe renal impairment (creatinine clearance [CrCL] < 30 mL/min) are not eligible; a calculated CrCl is acceptable CrCl ? 50 mL/min Renal: serum creatinine ?1.5 x ULN or creatinine clearance (CrCl) ?60 mL/min as calculated by the Cockroft-Gault method Creatinine clearance (CrCl) =< 40 mL/min Serum creatinine =< 1.5 mg/dL OR measured creatinine clearance (CrCl) >= 45 mL/min as calculated by the Cockcroft-Gault method OR 24-hour measured urine CrCl >= 45 mL/min CrCl (Creatinine Clearance) is >= 15 ml/min (<= 7 days prior to enrollment) Creatinine ? 1.5 x ULN or creatinine clearance (CrCl) ? 60 mL/min Renal: Creatinine clearance (CrCl) > 50 ml/min (measured or calculated/estimated). Serum creatinine ?1.5x the ULN or creatinine clearance (CrCl) ?50 mL/min. Serum creatinine (Cr) =< 1.5 X ULN or creatinine clearance (CrCl) >= 50 ml/min Within 14 days of the first dose of study drug: Serum creatinine =< 1.5 times the upper limit of normal or estimated creatinine clearance (CrCL) > 40 mL/min Serum creatinine =< 1.5 x ULN or creatinine clearance (CrCl) >= 40 mL/min Creatinine clearance (CrCl) >= 50 mL/min calculated by the Cockroft-Gault Creatinine clearance (CrCl) must be > 20 mL/min Calculated creatinine clearance (CrCl) > 30 mL/min Calculated or measured creatinine clearance (CrCl) > 30 ml/min Creatinine clearance (CrCl) value of >= 60 ml/min by MDRD study equation Serum creatinine =< 1.5 x ULN or creatinine clearance (CrCl) >= 40 mL/min Serum creatinine =< 1.5 times the upper limit of normal or estimated creatinine clearance (CrCl) > 40 mL/min within 14 days of the first dose of study drug Creatinine clearance (CrCl) > 45 mL/min Per MDACC Creatinine clearance guidelines, patients must have a Creatinine clearance > 50 ml/min determined by 24 hour collection or nomogram: CrCl male = (140 - age) x (wt in kg)/serum Cr x 72 CrCl female = 0.85 x (CrCl male) Serum creatinine =< 1.5 x ULN, or measured creatinine clearance (CrCl) >= 45 mL/min as calculated by the Cockcroft-Gault method or 24-hour measured urine CrCl >= 45 mL/min Serum creatinine > 1.5 x upper limit of normal or estimated creatinine clearance (CrCl) < 45 ml/min Serum creatinine =< 1.5 x upper limit of normal (ULN) or serum creatinine clearance (CrCl) >= 40 ml/min Serum creatinine normal for age or calculated creatinine clearance (CrCl) >= 70 ml/min/1.73 m^2 Creatinine =< 1.5 x ULN and concurrent creatinine clearance (CrCl) >= 50 mL/min/1.73 m^2 for patients with creatinine (Cr) > 1.5 x ULN DOSE ESCALATION COHORT: Serum creatinine ? 1.5 X ULN or creatinine clearance (CrCl) ? 50ml/min DOSE EXPANSION COHORT: Serum creatinine ? 1.5 X ULN or CrCl ? 50 ml/min Renal function: CrCl < 15 ml/min. Serum creatinine =< 2.0 x upper limit of normal (ULN) or serum creatinine clearance (CrCl) >= 40 ml/min Serum creatinine clearance (CrCl) >= 30 ml/min Creatinine clearance (CrCL) (calculated creatinine clearance is permitted) > 40 mL/min CrCL >= 40 ml/min Calculated creatinine clearance (CrCl) > 30 mL/min Renal: Serum Creatinine ? 1.5 x ULN or creatinine clearance (CrCl) ? 60 mL/min as calculated by the Cockroft-Gault method Creatinine =< 2 x ULN or creatinine clearance (CrCl) > 30 ml/min Patients deemed to have severe renal impairment should not be considered for this study; patients with creatinine clearance (CrCl) of < 40 mL/min should be excluded Renal: Serum Creatinine ? 1.5 x ULN or creatinine clearance (CrCl) ? 60 mL/min as calculated by the Cockroft-Gault method Serum creatinine =< 2 md/dL or estimated creatinine clearance (CrCl) > 50ml/min/body surface area (BSA) Calculated creatinine clearance (CrCL) of ? 45 mL/min Creatinine clearance (CrCl) >= 30 mL/min Serum creatinine ? 1.5 × upper limit of normal (ULN) or creatinine clearance (CrCl) ? 40 mL/min/1.73 m Creatinine clearance (CrCL) >= 25 ml/min Creatinine =< 1.5 x ULN or creatinine clearance (CrCl) calculated CrCl >= 60 mL/min/1.73m^2 Creatinine =< 2 x ULN or creatinine clearance (CrCl) > 30 ml/min Calculated or measured creatinine clearance (CrCl) of ? 30 mL/min Creatinine clearance; calculated creatinine clearance (CrCl) >= 30 mL/min and < 60 mL/min (Cockroft-Gault) unless the patient qualified based on hearing loss or neuropathy Calculated creatinine clearance (CRCL) > 60 mL/min Creatinine clearance (CrCl) > 50 mL/min Patients with severe renal impairment (creatinine clearance [CrCl] < 30 mL/min); a calculated CrCl is acceptable Serum creatinine of ?1.5 × the upper limit of normal (ULN)OR estimated creatinine clearance (CrCl) ? 40 ml/min/1.73 m2 Previous inability to tolerate full-dose lenalidomide, adjusted to creatinine clearance (CrCl) according to Cockroft-Gault at the time of previous lenalidomide treatment (25 mg day 1-21 every 28 days if CrCl >= 60 ml/min, 10 mg lenalidomide days (d) 1-21 every 28 days if CrCl < 60 mL/min but >= 30 mL/min, lenalidomide 15 mg every 48 hours (h) d1-21 every 28 days if CrCl < 30 mL/min but not requiring dialysis, lenalidomide 5 mg daily, day 1-21 every 28 days if CrCl < 30 mL/min and requiring dialysis Creatinine clearance (CrCl) < 30mL/min Creatinine (Cr) =< 1.5 mg/dL x upper limit of normal (ULN), creatinine clearance (CrCl) >= 50 mL/min calculated by the Cockroft-Gault method Serum creatinine =< 2.0 x upper limit of normal (ULN) or serum creatinine clearance (CrCl) >= 40 ml/min (drug is not cleared by the kidney) Serum creatinine =< 1.5 x ULN or creatinine clearance (CrCl) of >= 30 Serum creatinine < ULN OR calculated creatinine clearance (CrCl) of ? 60 ml/min Serum creatinine < 1.5 x upper limit of normal (ULN) or serum creatinine clearance (CrCl)> 40ml/min (CrCl= Wt (kg) x (140-age)*/72 x Cr. level, *female x 0.85) Serum creatinine < 2 or calculated creatinine clearance (CrCl) >= 30 mL/min Calculated or measured creatinine clearance (CrCl) >= 30 mL/min Renal impairment at baseline as measured by serum creatinine clearance (CrCl) ?60 mL/min ?21 days prior to registration. A measured or estimated creatinine clearance (CrCl) ?60 mL/min/1.73 m2 A calculated creatinine clearance (CrCl) that meets entry criteria for enrollment (ie, calculated CrCl either ? 90 or < 30 mL/min CrCl ? 30 mL/min as measured by 24-hour urine Donor must have adequate renal function as defined by a minimum creatinine clearance (CrCl) value of >30 ml/min. Severe renal impairment: estimated creatinine clearance (CrCl) <30 ml/min, but not requiring dialysis Normal renal function: estimated CrCl ?90 ml/min MDRD calculated or measured CrCl of ?30 mL/min MDRD calculated or measured CrCl of ?30 mL/min Serum creatinine =< 1.5 x ULN or creatinine clearance (CrCl) >= 40 mL/min Serum creatinine < 1.5 mg/dl and/or calculated or measured creatinine clearance (CrCl) >= 30 ml/min CrCL ? 40 mL/min Creatinine > 1.5 x ULN or creatinine clearance levels (CrCL) < 45 mL/min Estimated creatinine clearance (CrCl) >= 30 ml/min Creatinine clearance (CrCl) < 30 ml/min Creatinine clearance (CrCl) >= 30 milliliter per minute (mL/min) Patients with impaired renal function creatinine clearance (CRCL) =< 60 mL/min Creatinine =< 2 x ULN or creatinine clearance (CrCl) > 30 ml/min Creatinine ? 1.5 x ULN or CrCl > 60 mL/min/1.73 m2 for patients with serum creatinine levels above institutional 1.5 x ULN Measured or calculated creatinine clearance (CrCl; GFR can also be used in place of CrCl) >= 30 mL/min