A Trial Comparing Chemotherapy Versus Novel Immune Checkpoint Inhibitor (Pembrolizumab) Plus Chemotherapy in Treating Relapsed/Refractory Classical Hodgkin Lymphoma

Inclusion Criteria: * Patient must be \>= 5 years of age and =\< 75 years of age * Patient must have relapsed/refractory classical Hodgkin lymphoma (R/R cHL) after frontline (first line of chemotherapy) as evidenced by Fludeoxyglucose F-18 (FDG) avid on PET scan. If regimen is adjusted based on PET2 results or toxicity during frontline therapy, this will only be considered one line of therapy. Prior checkpoint inhibitor is completed \> 6 months prior to randomization * Patients \>= 18 years of age must have an Eastern Cooperative Oncology Group (ECOG) Performance Status of 0-2. Pediatric patients (16-17 years of age) must have a Karnofsky performance level \>= 50%. Pediatric patients (5-15 years of age) must have a Lansky performance level \>= 50 * Patient must be deemed fit for high dose chemo and autologous stem cell transplant * Patient must have the ability to understand and the willingness to sign a written informed consent document. Pediatric patients (\< 18 years of age) and patients with impaired decision-making capacity (IDMC) who have a legally authorized representative (LAR) or caregiver and/or family member available will also be considered eligible. Child assent must be obtained as appropriate in accordance with institutional guidelines * Absolute neutrophil count (ANC) \>= 1000/mcL (must be obtained =\< 7 days prior to randomization) * If disease includes marrow involvement or hypersplenism, please reference the below revised requirement: * ANC \>= 500/…