Brentuximab Vedotin + Rituximab as Frontline Therapy for Pts w/ CD30+ and/or EBV+ Lymphomas

Inclusion Criteria: * Histologically confirmed CD30+ and/or EBV+ lymphoid malignancy; in addition, there must be evidence of CD20 expression (at any level) * In cases of post-transplant lymphoproliferative disorder (PTLD) arising in patients who are pharmacologically immunosuppressed, reduction of immunosuppression (RI) must be attempted prior to or in conjunction with enrollment, with the exception of those for whom RI would pose excessive threat of clinically significant graft rejection (as judged by local investigator) * No prior chemotherapy or radiotherapy for PTLD or diffuse large B-cell lymphoma (DLBCL), with the exception of corticosteroids for 10 or fewer days at any dose (no washout period required) * No prior surgical intervention, unless performed for the sake of tissue diagnosis or on an urgent basis for disease-related threat to life, limb, or organ function * Bi-dimensionally measurable disease (at least 1 cm) * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Absolute neutrophil count \>= 750/mcL * Platelets \>= 50,000/mcl * Total bilirubin =\< 2 X institutional upper limit of normal (ULN) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum pyruvate glutamate transaminase \[SPGT\]) =\< 3 X institutional ULN * Creatinine =\< 2 X institutional ULN * NOTE: Patients who do not meet the above criteria because of disease involvement of the organ in question, or because of acute systemic illness due to lymphoma, may enroll with permission of the study Principal Investigator (PI) and approval from the Data Monitoring Committee; this flexibility be allowed due to the heterogeneity of the patient population, the wide range of complications seen in the initial presentation of EBV-related malignancy, and the frequent difficulty encountered in attempting to clearly document that organ dysfunction is the result of an underlying lymphoproliferative disorder * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 90 days following completion of therapy; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * A female of child-bearing potential is any woman (regardless of sexual orientation, having undergone a tubal ligation, or remaining celibate by choice) who meets the following criteria: * Has not undergone a hysterectomy or bilateral oophorectomy; or * Has not been naturally postmenopausal for at least 12 consecutive months (i.e., has had menses at any time in the preceding 12 consecutive months) * Patients must be free of any prior malignancies for \>= 1 year; NOTE: the exception to this would be currently treated squamous cell and basal cell carcinoma of the skin, carcinoma in situ of the cervix, breast, or bladder, or surgically removed melanoma in situ of the skin (stage 0) with histologically confirmed free margins of excision; in addition, it is well-recognized that patients at highest risk for EBV-related lymphoma (ie, those with chronic immunosuppression) are also at high risk for various malignancies, both invasive and non-invasive; therefore, exceptions may also be granted on a case-by-case basis, at the discretion of the PI with approval from the Data Monitoring Committee, for those patients with good clinical control of active malignancy, if the EBV-related lymphoma is considered to be a more immediate threat to the subject's health and/or life * Ability to understand and the willingness to sign a written informed consent; all patients must have signed, witnessed informed consent prior to registration Exclusion Criteria: * Chemotherapy (including monoclonal antibodies) or radiotherapy, administered for any condition, within 4 weeks prior to entering the study or incomplete recovery from adverse events due to agents administered more than 4 weeks earlier * Ongoing treatment with any other investigational agents * Known central nervous system (CNS) involvement of lymphoma * History of allergic reactions attributed to compounds of similar chemical or biologic composition to brentuximab vedotin and/or rituximab * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Known human immunodeficiency virus (HIV) infection * Known John Cunningham (JC) virus infection and/or progressive multifocal leukoencephalopathy (PML) * Clinically active hepatitis A, B, or C infections; NOTE: patients with chronic hepatitis C (HCV) or hepatitis B (HBV) infection may enroll if other laboratory criteria are met; those with HBV surface antigen positivity may enroll only if maintained on appropriate suppressive antiviral therapy, per treating investigator's discretion, for the duration of enrollment in the trial * Pregnancy or active nursing of an infant