Doxorubicin Hydrochloride, Pembrolizumab, Vinblastine, and Dacarbazine in Treating Patients With Classical Hodgkin Lymphoma

Inclusion Criteria: * Patients must have cHL that has not been previously treated * Part A: Any stage * Part B: Must be stage 3 or 4 * Patients must be appropriate candidates for at least 2 cycles of doxorubicin hydrochloride (adriamycin), bleomycin, vinblastine and dacarbazine (ABVD) (6 cycles for Part B patients) or doxorubicin hydrochloride, vinblastine, dacarbazine (AVD) (this could include patients ranging from favorable risk early stage disease to poor prognosis advanced stage disease) * Patients must have measurable FDG-avid disease defined by standard criteria (Lugano 2014) and a minimum of 1.0 cm in diameter * Patients should not have evidence of active central nervous system lymphoma * Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Patients must have a left ventricular ejection (LVEF) \>= 50% within 56 days of enrollment * Patients must have adequate labs within 10 days of treatment * Absolute neutrophil count (ANC) \>= 1,500/mm\^3 (without transfusion or growth factor support) * Platelets \>= 100,000/mm\^3 (without transfusion or growth factor support) * Hemoglobin \>= 8 g/dL. Growth factor and/or transfusion support is permissible to stabilize participant prior to study treatment if needed. There is no lower limit to cytopenias if related to bone marrow involvement * Serum creatinine \< 1.5 mg/dl or creatinine clearance greater than 30/ml per minute by Cockcroft Gault formula * Total bilirubin =\< 1.5 times upper limit of normal OR direct bilirubin =\< upper limit of normal (ULN) for participants with total bilirubin levels \> 1.5 x ULN * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 times upper limit of normal (=\< 5 x ULN for participants with liver metastases) * All patients must be informed of the investigational nature of this study and have given written consent in accordance with institutional and federal guidelines * Patients must be anticipated to complete all planned study therapy * Male subjects should agree to use an adequate method of barrier contraception starting with the first dose of study therapy through 120 days after the last dose of study therapy * Female subject of childbearing potential should have a negative urine or serum pregnancy within 72 hours prior to receiving the first dose of study medication; if the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Female subjects of childbearing potential should be willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 120 days after the last dose of study medication; subjects of childbearing potential are those who have not been surgically sterilized or have not been free from menses for \> 1 year Exclusion Criteria: * Patients known positive for human immunodeficiency virus (HIV), or infectious hepatitis type B or C * Pregnant or nursing women; men or women of reproductive potential may not participate unless they have agreed to use an effective contraceptive method * Patients with other prior malignancies except for adequately treated basal cell carcinoma, squamous cell carcinoma of the skin, breast or cervical cancer in situ, or other cancer from which the patient has been disease-free for 5 years or greater, unless approved by the protocol chair or co-chair * Patients who have other medical conditions that would contraindicate treatment with aggressive chemotherapy (including active infection, uncontrolled hypertension, congestive heart failure, unstable angina pectoris, or myocardial infarction within the past 6 months, uncontrolled arrhythmia, severe pulmonary disease or requirement of supplemental oxygen) * Active ischemic heart disease or congestive heart failure * Concurrent use of other anti-cancer agents or experimental treatments * Known current or prior autoimmune disease with the exception of vitiligo * Active or prior history of pneumonitis/interstitial lung disease that required corticosteroids * Current use of supplemental oxygen * Is known to have received a live vaccine or live-attenuated vaccine within 30 days prior to the first dose of trial treatment. Administration of killed vaccines is allowed