Romidepsin and Parsaclisib for the Treatment of Relapsed or Refractory T-Cell Lymphomas

Inclusion Criteria: * Age \>= 18 years * Able to understand and voluntarily sign a consent form * Biopsy proven diagnosis of PTCL or CTCL * Relapsed/refractory PTCL, progressing after at least one line of systemic therapy (for anaplastic large cell lymphoma \[ALCL\], must have had prior treatment with brentuximab vedotin). OR * Relapsed/Refractory CTCL, that progressed on at least 2 lines of skin-directed (topical) therapy and/or one line of systemic therapy. Pre-treatment with mogamulizumab and/or brentuximab vedotin (in the presence of CD30 positive disease) is NOT required as a criterion for eligibility. Skin-directed therapies include, but are not limited to topical steroids, topical chemotherapy, imiquimod, narrow band ultraviolet B (UVB), psoralen plus ultraviolet A photochemotherapy (PUVA), total skin electron beam radiation, and extracorporeal photopheresis * Mycosis fungoides with large cell transformation is eligible * Performance status (Eastern Cooperative Oncology Group \[ECOG\]) 0-2 * Life expectancy \>= 90 days * Patient must have at least stage IB CTCL (\> 10% eBSA) or PTCL with disease defined by a nodal area of at least 1.5 cm in long dimension, extranodal disease of at least 1 cm in long dimension, or fludeoxyglucose F-18 - positron emission tomography (FDG-PET) avid disease (Deauville score = 5) * Absolute neutrophil count (ANC) \>= 1,000/mm\^3 * Platelet count \>= 100,000/mm\^3 * Calculated creatinine clearance \>= 50mL/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. If the subject has Gilbert's disease, low-grade hemolysis, or liver involvement with lymphoma, a bilirubin level of =\< 4 x ULN will be allowed * Negative serum pregnancy test at the time of enrollment for females of childbearing potential * Women of childbearing potential (as defined as a sexually mature woman who: 1) has not undergone a hysterectomy or bilateral oophorectomy or 2) has not been naturally postmenopausal for at least 24 consecutive months) are required to use a highly effective method of contraception (i.e. intrauterine device \[IUD\], hormonal \[birth control pills, injections, or implants\] while on study). Male patients engaged in a sexual relationship with a woman of childbearing potential must agree to use a latex condom during sexual contact, even if he has had a successful vasectomy * All cancer therapy, including radiation, topical steroid, and chemotherapy must have been discontinued at least 1 week or 3 half-lives whichever is the longest prior to treatment in this study. The only exceptions are participants who are symptomatic from their skin lesions and have been on corticosteroids for prolonged periods of time (\> 60 days) without change may continue use of either systemic steroids (equivalent to \< 10 mg per day of prednisone) or topical steroids are eligible for this study if the frequency and dosage steroids has not changed for 14 days prior to the study Exclusion Criteria: * Patients with uncontrolled central nervous system (CNS) disease * Use of immunosuppressive therapy within 28 days of randomization. Immunosuppressive therapy includes, but is not limited to, cyclosporine A, tacrolimus, or high-dose corticosteroids. Participants receiving corticosteroids must be at a dose of =\< 10 mg/day prednisone (or equivalent) within 7 days of randomization. However, topical steroids (maximum strength Class III according to World Health Organization Classification of Topical steroids) are allowed to control pruritis * An active infection requiring a systemic antimicrobial. The patient should be off antibiotic treatment for an active infection for 7 days prior to enrollment in the trial. However, antibiotic prophylaxis is acceptable as long as the dose of the medication has been stable for at least 7 days prior to the baseline exam * Exposure to a live vaccine within 30 days of treatment start * Positive at the time of screening for human immunodeficiency virus (HIV), hepatitis B surface antigen or viral load, hepatitis C viral load. Hepatitis B (HBV) or hepatitis C (HCV) infection: Participants positive for HBV surface antigen or HBV core antibody will be eligible if they are negative for HBV-deoxyribonucleic acid (DNA); these participants should be considered for prophylactic antiviral therapy. Participants positive for anti-HCV antibody will be eligible if they are negative for HCV ribonucleic acid (RNA) * Prior malignancy within the past 2 years (allowing squamous cell and basal cell carcinomas with free margins at excision) * Prior treatment with a PI3K inhibitor * Presence of an abnormal electrocardiogram (ECG) that is clinically meaningful. Screening corrected QT interval (QTc) interval \> 450 milliseconds is excluded (corrected by Fridericia). In the event that a single QTc is \> 450 milliseconds, the participant may enroll if the average QTc for 3 ECGs is \< 450 milliseconds. If left bundle branch is present, upper limit of QTc will be 550 milliseconds * Use of strong CYP3A4 inhibitors and inducers. If a CYP3A4 inhibitor was recently used, there should be 14 days or 5 half-lives time (whichever is longer) before the first dose of parsaclisib is administered. Use of moderate CYP3A4 inhibitors are strongly discouraged but not strictly prohibited. If a strong CYP3A4 inhibitor is started after study enrollment, the study principal investigator (PI) should be contacted to discuss alternatives * Unable to swallow tablets, disease significantly affecting gastrointestinal function, or resection of the stomach or small bowel or ulcerative colitis, symptomatic inflammatory bowel disease, or partial or complete bowel obstruction likely to interfere with the delivery, absorption, or metabolism of parsaclisib * Clinically significant history of liver disease, including viral or other hepatitis, current alcohol abuse, or cirrhosis * Progression while on romidepsin or within 3 months of discontinuation of romidepsin. Prior treatment with romidepsin is allowed if it was well-tolerated * Unwillingness to comply with study procedures, including follow-up, as specified by this protocol, or unwillingness to cooperate fully with the investigator * Pregnant or lactating, or intending to become pregnant during the study * Clinically significant abnormalities in medical history, physical examination, or laboratory values, which in the opinion of the investigator would make the patient unsuitable for inclusion in the study