Inclusion Criteria:

          -  Age >= 18 years

          -  Newly diagnosed, untreated, histologically confirmed diffuse large B-cell lymphoma
             expressing the CD20 antigen, with ANY of the following:

               -  Non-germinal center B-cell (GCB) subtype by Hans algorithm

               -  Myc expression >= 40% by immunohistochemistry (IHC)

               -  Bcl-2 expression >= 50% by IHC

               -  Myc expression >= 40% AND Bcl-2 expression >= 50% by IHC (double expressor)

               -  MYC rearrangement by fluorescence in situ hybridization (FISH)

               -  Or high-grade B-cell lymphoma with MYC rearrangement AND BCL2 and/or BCL6
                  rearrangement (double-hit or triple-hit lymphoma) but not a candidate for more
                  aggressive chemotherapy (such as cyclophosphamide, Oncovin [vincristine],
                  doxorubicin, [CODOX]-methotrexate [M]- ifosfamide, Vepesid [etoposide], Ara-C
                  [cytarabine] [IVAC])

                    -  NOTE: Patients with a new diagnosis of concurrent DLBCL and an indolent
                       lymphoma (previously undiagnosed, such as follicular lymphoma or marginal
                       zone lymphoma) are eligible. However, patients with a known prior diagnosis
                       of indolent lymphoma with new transformation to DLBCL (i.e., transformed
                       lymphoma) are not eligible

          -  Ann Arbor stages II (bulky disease, i.e., >= 5 cm, or not a candidate for combined
             modality treatment with R-CHOP plus radiotherapy), III, or IV

          -  Measurable disease (at least 1 lesion of >= 1.5 cm in one diameter) as detected by
             computed tomography (CT) or the CT images of PET/CT. Skins lesions can be used if the
             area is >= 2 cm in at least one diameter and photographed with a ruler

          -  Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1 or 2

          -  Absolute neutrophil count (ANC) >= 1500/mm^3 (obtained =< 14 days prior to
             registration)

          -  Platelet count >= 100,000/mm^3 (obtained =< 14 days prior to registration)

          -  Total bilirubin =< 1.5 x upper limit of normal (ULN), or if total bilirubin is > 1.5 x
             ULN, the direct bilirubin must be normal (obtained =< 14 days prior to registration)

          -  Aspartate transaminase (AST) =< 3 x ULN (=< 5 x ULN for patients with direct liver
             involvement by lymphoma) (obtained =< 14 days prior to registration)

          -  Alkaline phosphatase =< 3 x ULN, unless evidence of the direct liver involvement by
             lymphoma, then =< 5 x ULN (obtained =< 14 days prior to registration)

          -  Calculated creatinine clearance of >= 30 mL/min using the Cockcroft-Gault formula
             (obtained =< 14 days prior to registration)

          -  Negative urine pregnancy test done =< 7 days prior to registration, for persons of
             childbearing potential only

               -  NOTE: If the urine test is positive or cannot be confirmed as negative, a serum
                  pregnancy test will be required

          -  Persons of childbearing potential must agree to use one reliable form of birth control

          -  Provide written informed consent

          -  Willingness to provide mandatory research blood specimens for banking

          -  Willing to return to enrolling institution for follow-up (during the Active Monitoring
             Phase of the study)

        Exclusion Criteria:

          -  Any of the following because this study involves an investigational agent whose
             genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are
             unknown:

               -  Pregnant persons

               -  Nursing persons (lactating persons are eligible provided that they agree not to
                  breast feed while taking parsaclisib)

               -  Persons of childbearing potential who are unwilling to employ adequate
                  contraception

          -  Primary central nervous system (CNS) lymphoma, or parenchymal, meningeal or
             cerebrospinal fluid involvement with malignant lymphoma cells

          -  Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment
             of the investigator, would make the patient inappropriate for entry into this study or
             interfere significantly with the proper assessment of safety and toxicity of the
             prescribed regimens

          -  Immunocompromised patients and patients known to be human immunodeficiency virus (HIV)
             positive and currently receiving antiretroviral therapy (except for patients on
             effective antiretroviral therapy with undetectable viral load within 6 months)

               -  NOTE: If evidence of chronic hepatitis B virus (HBV) infection, HBV viral load
                  must be undetectable on suppressive therapy if indicated

               -  NOTE: If history of hepatitis C virus (HCV) infection, HCV viral load must be
                  undetectable

          -  Uncontrolled intercurrent illness including, but not limited to:

               -  Ongoing or active infection

               -  Symptomatic congestive heart failure requiring use of ongoing maintenance therapy
                  for life-threatening ventricular arrhythmias

               -  Unstable angina pectoris

               -  Cardiac arrhythmia

               -  Ongoing inflammatory bowel disease (such as ulcerative colitis) or other colitis
                  requiring active treatment

               -  Oxygen dependent baseline lung disease (such as interstitial lung disease or
                  chronic obstructive pulmonary disease [COPD])

               -  Or psychiatric illness/social situations that would limit compliance with study
                  requirements

          -  Received or receiving any other agent which would be considered as a treatment for the
             lymphoma (with the exception of corticosteroid)

          -  Other active malignancy requiring therapy such as radiation, chemotherapy or
             immunotherapy. Patients on hormonal therapy for treated breast or prostate cancer are
             permitted if they meet other eligibility criteria

               -  EXCEPTIONS: Localized non-melanotic skin cancer or any cancer that in the
                  judgment of the investigator has been treated with curative intent (e.g.,
                  disease-free survival equal or more than 5 years) and will not interfere with the
                  study treatment plan and response assessment

               -  NOTE: If there is a history of prior malignancy, they must not require therapy
                  such as radiation, chemotherapy or immunotherapy for their cancer

          -  History of myocardial infarction =< 6 months, or congestive heart failure requiring
             use of ongoing maintenance therapy for life-threatening ventricular arrhythmias

          -  >= 25% of bone marrow radiated for other diseases

          -  Ejection fraction of < 45% by either multigated acquisition scan (MUGA) or
             echocardiogram (ECHO)