Epcoritamab in Combination With Dose Adjusted EPOCH-R for High-risk Burkitt Lymphoma (BL), The BEDROCK Study

Inclusion Criteria: * Histologically and immunophenotypically (via at least a core or ideally, incisional or excisional biopsy) documented BL at the treating institution. All stages of BL are eligible * High-risk adult BL patients, as defined by: * Stage I with any ONE of the following: * A single lesion 10 cm or greater * Elevated lactate dehydrogenase (LDH) * Total resection of intra-abdominal disease with an elevated LDH after surgery OR * Stage II or higher * Either of the above PLUS ANY one of the following additional risk factors: * Involvement of the bone marrow * Involvement by the peripheral blood by morphology or flow cytometry * Presence of leptomeningeal disease * Age ≥ 40 years * Lactate dehydrogenase \> 3× upper limit of normal (ULN) * Eastern Cooperative Oncology Group (ECOG) performance status 2-3 * Treatment naive or one prior cycle of chemotherapy whether anthracycline based or not * If HIV positive and had an opportunistic infection within three months, participant must be recovered and willing to take prophylaxis as clinically indicated * If HIV positive, any CD4 count is acceptable * A minimum of two HIV-positive participants will be enrolled in Cohort 1 and a minimum of 10 HIV-positive participants will be enrolled in the randomized cohort. Once 18 HIV-negative participants are enrolled, future enrollment will allow only HIV-positive participants * Known HIV status. Participants may be HIV positive, with documentation of HIV infection by means of any one of the following: * Documentation of HIV diagnosis in the medical record by a licensed health care provider * Documentation of receipt of highly active antiretroviral therapy (HAART) (at least three different medications) by a licensed health care provider (documentation may be a record of a HAART prescription in the participant's medical record, a written prescription in the name of the participant for HAART, or pill bottles for HAART with a label showing the participant's name) * HIV-1 ribonucleic acid (RNA) detection by a licensed HIV-1 RNA assay demonstrating \> 1000 RNA copies/mL * Any licensed HIV screening antibody and/or HIV antibody/antigen combination assay confirmed by a second licensed HIV assay such as a HIV-1 Western blot confirmation or HIV rapid multispot antibody differentiation assay * NOTE: A "licensed" assay refers to a United States Food and Drug Administration (FDA)-approved assay, which is required for all Investigational New Drug (IND) studies * Participants without HIV infection must have evidence of a negative result using any licensed HIV screening antibody assay and/or HIV antibody/antigen combination assay within 12 months before enrollment * If HIV positive, participant should have concurrent treatment with effective HAART or intend to start HAART shortly after enrollment * Measurable disease (unless marrow-only disease is present), defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter) as ≥ 15 mm (≥ 1.5cm) by computed tomography (CT) or positron emission tomography (PET) scan or calipers by clinical exam or evaluable by bone marrow. Tumor measurement can be assessed by treating physician. An official radiology reading does not need to be completed prior to enrollment * Adequate cardiac function defined as an ejection fraction on echocardiogram (ECHO) or multigated acquisition (MUGA) scan that is at or above 45% within six weeks before enrollment * Age ≥ 18 years * ECOG performance status ≤ 3. Patients with ECOG 3 must have poor performance status secondary to BL * Absolute neutrophil count: ≥ 1,000/mcL unless attributed to BL (assessed within 2 weeks of enrollment) * Platelets: ≥ 100,000/mcL unless attributed to BL (assessed within 2 weeks of enrollment) * Total bilirubin: ≤ institutional upper limit of normal (ULN) (assessed within 2 weeks of enrollment) unless attributed to Gilbert's on antiretroviral therapy (ART) in which case the direct bilirubin should be \< institutional ULN * Aspartate aminotransferase (AST)(serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT)(serum glutamic pyruvate transaminase \[SGPT\]): ≤ 3 × institutional ULN (assessed within 2 weeks of enrollment), or if attributed to hepatic involvement by BL, the direct bilirubin should be \< 2x institutional ULN and the AST(SGOT)/ALT(SGPT): ≤ 5 × institutional ULN * Creatinine: ≤ institutional ULN OR glomerular filtration rate (GFR): ≥ 50 mL/min/1.73 m\^2 (assessed within 2 weeks of enrollment) * All participants will be required to be screened for hepatitis B. Participants with resolved infection (i.e., participants who are hepatitis B surface antigen negative but positive for antibodies to hepatitis B core antigen and/or antibodies to hepatitis B surface antigen must be screened using real-time polymerase chain reaction (PCR) measurement of hepatitis B virus (HBV) DNA levels. Participants who are hepatitis B core positive or PCR positive must begin suppressive therapy. Participants with hepatitis B or PCR positivity must be followed by a hepatologist for serial testing. EXCEPTION: Participants with serologic findings suggestive of HBV vaccination (hepatitis B core antigen positivity as the only serologic marker) AND a known history of prior HBV vaccination, do not need to be tested for HBV DNA by PCR * For participants with evidence of chronic HBV infection, the HBV viral load must be undetectable on suppressive therapy, if indicated * Participants with a history of hepatitis C virus (HCV) infection previously treated and cured are eligible. For participants with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load. Participants incidentally found to have hepatitis C during screening with a measurable HCV viral load are not eligible * Participants with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial * Participants with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, participants should be class II or better * Ability to understand and the willingness to sign a written informed consent document. Legally authorized representatives may sign and give informed consent on behalf of study participants * Women of childbearing potential and men must be willing to use contraception during the study treatment and for four months after the last dose of study drug and agree to inform treating physician immediately of suspected pregnancy Exclusion Criteria: * Brain or spinal cord parenchymal disease * Prior cytotoxic chemotherapy or radiotherapy for this lymphoma other than the following: * Palliative radiation for medical emergencies (like cord compression) * A maximum of one cycle of combination chemotherapy, including EPOCH or cyclophosphamide, doxorubicin, vincristine, and prednisone (CHOP)-like therapy. The start of the previous chemotherapy cycle must occur at least 21 days but no more than four weeks prior to the beginning of therapy under this protocol, and such cycle will count towards the maximum of six cycles under this study (i.e., cycle off study will count as Cycle 1). OR * One prior cycle of limited therapy including cyclophosphamide and/or glucocorticoids to improve performance status or hepatic or renal function impaired due to lymphoma involvement. The start of this therapy may occur up to four weeks prior to the beginning of study treatment under this protocol. Cyclophosphamide administration must have been completed at least 14 days prior to initiation of study treatment. Such treatment will not count towards the maximum of six cycles under this study (i.e., participants will receive six cycles on study) * Participants with refractory HIV disease will not be eligible. Refractory HIV will be defined as prior ART exposure and HIV viral load \> 1000 copies/uL and no options for HIV control evaluated by HIV genotyping. Participants with HIV viral load \> 1000 copies/uL can be enrolled if additional ART will be initiated * Any prior exposure to liposomal doxorubicin is allowed as long as the left ventricular ejection fraction (LVEF) is ≥ 45%. It is at the discretion of the investigator if prior exposure to doxorubicin for an unrelated malignancy is acceptable * Participants with peripheral neuropathy Grade ≥ 3 or neuropathic pain Grade ≥ 2 * Participants with known brain metastases from solid tumors will be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events (AEs) * Participants with Hepatitis C (Hepatitis C antibody positive) with cirrhosis, whether Hepatitis C RNA level is measurable or not * History of allergic reactions, hypersensitivity, or intolerance attributed to compounds of similar chemical or biologic composition to agents used in the study * Participants must not have any condition that would make participation in this protocol unduly hazardous * A pregnancy test must be performed within seven days prior to therapy administration in women of childbearing potential. Pregnant women are excluded from this study because the effects of epcoritamab on the developing human fetus are unknown. Because there is an unknown but potential risk for AEs in nursing infants secondary to treatment of the mother with bispecific antibodies and chemotherapy, breastfeeding should be discontinued prior to treatment initiation and will not be permitted during treatment and for four months after the final treatment dose. Both male and female participants must use effective methods of birth control during the course of the study and for three months after stopping treatment. Participants must also agree to not donate eggs or sperm while taking the study drugs and for three months after stopping * Unable to provide adequate informed consent in the opinion of the Principal Investigator (PI) * Major surgery, other than diagnostic surgery, occurring within four weeks prior to study entry. Splenectomy will not be considered an exclusionary major surgery * Myocardial infarction within six months prior to study entry, New York Heart Association Class II or greater heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, clinically significant pericardial disease, or electrocardiographic evidence of acute ischemic or active conduction system abnormalities * Known chronic obstructive pulmonary disease (COPD) with a forced expiratory volume in one second (FEV1) is \< 50% of predicted normal. Note that FEV1 testing also is required for participants suspected of having COPD and participants must be excluded if FEV1 is \< 50% of predicted normal * Known moderate or severe persistent asthma, or a history of asthma within the last two years, or currently has uncontrolled asthma of any classification. Participants who currently have controlled intermittent asthma or controlled mild persistent asthma are allowed to participate in the study * Participants who are receiving any other investigational agents * History of allergic reactions attributed to compounds of similar chemical or biologic composition to epcoritamab, or other agents used in this study * Participants on cobicistat, indinavir, or ritonavir, or agents that are strong CYP3A4 inhibitors as these increase the toxicity of doxorubicin and vincristine. If on a strong CYP3A4 inhibitor regimen prior to study enrollment, participants must be switched to alternative drugs ideally one week prior to administration of study therapy. Exceptions must be noted on the eligibility form. All concomitant medications must be reviewed by the study chair or co-chair prior to enrollment by email * Participants with uncontrolled intercurrent illness or any other significant condition(s) that would make participation in this protocol unreasonably hazardous