PET-Directed Therapy With Pembrolizumab and Combination Chemotherapy in Treating Patients With Previously Untreated Classical Hodgkin Lymphoma

Inclusion Criteria: * Patients must have a histologically confirmed diagnosis of classical Hodgkin lymphoma including nodular sclerosis, mixed cellularity, lymphocytic-rich, and lymphocyte depleted subtypes by the 4th edition of the World Health Organization (WHO) Classification of Tumors of Hematopoietic and Lymphoid Tissues published in 2008 (nodular lymphocyte-predominant Hodgkin lymphoma \[NLPHL\] excluded) * Patients must have measurable disease by the Lugano criteria * Patients must have previously untreated disease (except for one week or less of corticosteroids) * Patients must exhibit a/an Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 * Patients may have any stage and any International Prognostic Score (IPS) * Patients must have adequate organ and bone marrow function within 14 days prior to registration, as defined below: * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcl * Total bilirubin within normal institutional limits * Aspartate aminotransferase (AST)(serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT)(serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X institutional upper limit of normal (ULN) * Creatinine within normal institutional limits * Platelet transfusions are acceptable prior to treatment to achieve the above numbers, however growth factors are not allowed within 14 days of registration * Females of child-bearing potential (FOCBP) and males must agree to avoid becoming pregnant, or impregnating a partner, respectively, by complying with any of the approved contraception techniques prior to registration, for the duration of study participation, and for 120 days following completion of therapy; abstinence is acceptable if this is the usual lifestyle and preferred contraception for the subject; should a female patient become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately NOTE: A FOCBP 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 * Has had menses at any time in the preceding 12 consecutive months (and therefore has not been naturally postmenopausal for \> 12 months) * FOCBP must have a negative pregnancy test within 7 days prior to registration on study; NOTE: a negative pregnancy test is also required within 3 days prior to first dose of pembrolizumab and therefore may need to be repeated if screening test is more than 3 days prior to first dose * Patients must have the ability to understand and the willingness to sign a written informed consent prior to registration on study Exclusion Criteria: * Patients are not eligible who have had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to registration or who have not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to a previously administered agent * NOTE: Subjects with =\< grade 2 neuropathy are an exception to this criterion and may qualify for the study * NOTE: If subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy * Patients who have a diagnosis of immunodeficiency or are receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to registration are not eligible * Patients who have a known history of active TB (bacillus tuberculosis) are not eligible * Patients must not have a history of allergic reactions attributed to compounds of similar chemical or biologic composition to pembrolizumab * Patients who have an uncontrolled intercurrent illness including, but not limited to any of the following, are not eligible: * Symptomatic congestive heart failure * Unstable angina pectoris * Cardiac arrhythmia * Patients who have a known additional malignancy that is progressing or requires active treatment are not eligible * NOTE: Exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer * Patients who have known active central nervous system (CNS) metastases and/or carcinomatous meningitis are not eligible * NOTE: Subjects with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least four weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 7 days prior to registration; this exception does not include carcinomatous meningitis which is excluded regardless of clinical stability * Patients who have active autoimmune disease that has required systemic treatment in the past 2 years are not eligible (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs) * NOTE: Replacement therapy (e.g. thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment * Patients who have known history of, or any evidence of active, non-infectious pneumonitis are not eligible * Patients who have an active infection requiring systemic therapy are not eligible, except for uncomplicated urinary tract infections * Patients are not eligible who have a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject?s participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator * Patients who have known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial are not eligible * Patients may not be pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, from registration through 120 days after the last dose of trial treatment * Patients who have received prior therapy with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent are not eligible * Patients who have a known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies) are not eligible * Patients who have active hepatitis B (e.g., hepatitis B virus surface antigen \[HBsAg\] reactive) or hepatitis C (e.g., hepatitis c virus \[HCV\] ribonucleic acid \[RNA\] \[qualitative\] is detected) are not eligible * Patients who received a live vaccine within 30 days of planned start of study therapy are not eligible; examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster, yellow fever, rabies, bacillus Calmette-Guerin (BCG), and typhoid vaccine * NOTE: Seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist) are live attenuated vaccines, and are not allowed