Inclusion Criteria:

• Subjects must have histologically documented relapsed or refractory disease, with a diagnosis of one of the following lymphoid malignancies: Diffuse Large B-cell Lymphoma, Peripheral T-cell Lymphoma (any subtype). Subjects must have received at least one prior systemic chemotherapy and must have either received an autologous stem cell transplant, refused or been deemed ineligible for an autologous stem cell transplant
• Subjects must be willing and able to have a fresh tumor biopsy prior to start of study treatment for research evaluations. If insufficient fresh tissue is obtained to provide sub-classification for cohorts, then tissue material from a previous relapse biopsy and/or original diagnostic block may be requested
• Subjects must have measurable lesions (at least one target lesion of any size) by computerized tomography (CT) scan, and/or measurable lymphoma cutaneous lesions
• Eastern Cooperative Oncology Group (ECOG) performance status 0-2
• Absolute neutrophil count (ANC) ≥ 1,000/mm^3
• Platelet count ≥ 75,000/mm^3
• Hemoglobin ≥ 8.0 g/dL
• Serum creatinine ≤ 2.0 g/dL or calculated creatinine clearance ≥ 60mL/min (Cockcroft-Gault Method)
• Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 2.5 x institutional upper limit of normal (ULN) or ≤ 5 x ULN if liver involved by lymphoma
• Bilirubin < 2.0 x ULN unless subject has Gilbert's disease, low-grade hemolysis, or liver involvement with lymphoma
• At least 2 weeks since prior chemotherapy, biological therapy, radiation therapy, major surgery, other investigational, or anti-cancer therapy that is considered disease-directed and recovered from prior toxicities to Grade 0-1 at least 2 weeks prior to investigational therapy
• Females will be either postmenopausal for at least 1 year or surgically sterile for at least 3 months OR Females of child-bearing potential must have a negative pregnancy test at screening and agree to take appropriate precautions to avoid pregnancy from screening through follow-up
• Males must agree to take appropriate precautions to avoid fathering a child from screening through follow-up
• Able to comprehend and willing to sign an Informed Consent Form (ICF)

Exclusion Criteria:

• History of or active central nervous system (CNS) malignancy
• Allogeneic stem cell transplant within the last 6 months, or active-graft-versus-host disease following allogeneic transplant, or subjects currently on immunosuppressive therapy following allogeneic transplant
• Uncontrolled intercurrent illness including, but not limited to, ongoing active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situation that would limit compliance with study requirements as judged by treating physician; subjects receiving antibiotics that are under control may be included in the study
• Pregnant or breastfeeding women
• Clinically symptomatic and uncontrolled cardiovascular disease
• History of myocardial infarction, severe/unstable angina, or symptomatic congestive heart failure, within the 6 months prior to study drug administration
• Current or recent history (< 21 days prior to start of treatment) of a clinically significant bacterial, viral, fungal, parasitic or mycobacterial infection
• History of other malignancy, with the exception of squamous cell carcinoma of the skin, basal cell carcinoma of the skin, cervical intraepithelial neoplasia, or other malignancies that have been in remission for at least 3 years
• Presence of a malabsorption syndrome possibly affecting drug absorption (e.g., Crohn's disease or chronic pancreatitis)
• Any prior or concomitant use of another JAK inhibitor
• Known active hepatitis B or C, or human immunodeficiency virus (HIV) infection
• Subjects who, in the opinion of the Investigator, are unable or unlikely to comply with the dosing schedule and study evaluations