Testing the Addition of Duvelisib or CC-486 to the Usual Treatment for Peripheral T-Cell Lymphoma

Inclusion Criteria:

* Histologically confirmed diagnosis of peripheral T-cell lymphoma (PTCL) with \< 10% CD30 expression by immunohistochemistry in the following subtypes (by local review): nodal T-cell lymphoma with T-follicular helper (TFH) phenotype (TFH-PTCL), follicular T-cell lymphoma, PTCL-not otherwise specified (NOS), angioimmunoblastic T-cell lymphoma (AITL), enteropathy associated T-cell lymphoma, monomorphic epitheliotropic intestinal T-cell lymphoma

  * Patients with expression of CD30 in \>= 10% of the tumor (based on local immunohistochemistry review) regardless of histology will not be permitted
  * Patients with a diagnosis of other PTCL subtype histologies other than those specified in the inclusion criteria are excluded including large cell transformation of mycosis fungoides
  * Patients will be stratified by presence or absence of TFH phenotype (i.e. diagnosis of AITL, TFH-PTCL, follicular T-cell lymphoma) based on local review of pathology. Determination of TFH phenotype can be defined by expression of two or more of the following markers CD10, BCL6, CXCL13, ICOS, and PD1 by immunohistochemistry
* Measurable disease as defined by the Lugano criteria
* No prior systemic therapy for lymphoma (excluding corticosteroids)
* Not pregnant and not nursing, because this study involves an investigational agent whose genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are unknown. Therefore, for women of childbearing potential only, a negative urine or serum pregnancy test done =\< 7 days prior to registration is required
* Age \>= 18 years
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 2
* Platelet count \>= 75,000/mm\^3 (\>= 50,000/mm\^3 if secondary to bone marrow involvement from lymphoma per investigator assessment; the first 12 patients on each arm of the study must have platelets \>= 75,000/mm\^3 regardless of bone marrow involvement)
* Absolute neutrophil count (ANC) \>= 1,000/mm\^3
* Aspartate aminotransferase (AST)/serum glutamic-oxaloacetic transaminase (SGOT) or alanine aminotransferase (ALT)/serum glutamate pyruvate transaminase (SGPT) =\< 3.0 x upper limit of normal (ULN)

  \* Except in subjects with documented liver involvement by lymphoma
* Calculated creatinine clearance \>= 30 mL/min by Cockcroft-Gault formula
* Total bilirubin =\< 2.0 x ULN

  \* Except in cases of Gilbert's Syndrome or documented liver or pancreatic involvement by lymphoma
* Archival tissue must be available for submission
* Patients known to have HTLV 1/2 are excluded
* Patients with known central nervous system involvement are excluded
* No active viral infection with human immunodeficiency virus (HIV), hepatitis B, or hepatitis C. Those who are seropositive (e.g. hepatitis B core antibody \[Ab\] positive) are permitted if they are negative by polymerase chain reaction (PCR). Those who are seropositive for hepatitis B and are negative for hepatitis B virus (HBV) deoxyribonucleic acid (DNA) by PCR must receive concomitant hepatitis B directed antiviral therapy. Those who have hepatitis C Ab positivity who have completed curative therapy for hepatitis C with negative hepatitis C PCR are eligible
* Patients with history of HIV are eligible if they have an undetectable viral load for at least 6 months
* No active uncontrolled systemic fungal, bacterial or viral infection (defined as ongoing signs/symptoms related to the infection without improvement despite appropriate antibiotics, antiviral therapy and/or other treatment). Patients with Epstein-Barr virus (EBV) viremia related to their lymphoma are permitted
* No concurrent malignancy requiring active therapy within the last 3 years with the exception of basal cell carcinoma limited to the skin, squamous cell carcinoma limited to the skin, carcinoma in situ of the cervix, breast or localized prostate cancer. Adjuvant hormonal therapy for cancer previously treated for curative intent is permitted
* Patients must have documented left ventricular ejection fraction of \>= 45%
* No significant active cardiac disease within the previous 6 months including:

  * New York Heart Association (NYHA) class III or IV congestive heart failure
  * Unstable angina or angina requiring surgical or medical intervention; and/or
  * Myocardial infarction
* No contraindication to any drug in the chemotherapy regimen, including neuropathy \>= grade 2
* Chronic concomitant treatment with strong inhibitors of CYP3A4 is not allowed on this study. Patients on strong CYP3A4 inhibitors must discontinue the drug for 14 days prior to registration on the study. Chronic concomitant treatment with strong CYP3A4 inducers is not allowed. Patients must discontinue the drug 14 days prior to the start of study treatment