Inclusion Criteria:
* Age \>= 18 years
* Biopsy-proven relapsed or refractory lymphomas; relapsed is defined as a relapse that occurred after having a response to the last therapy that lasted \> 6 months; refractory is no response or relapse within 6 months; previous biopsies \< 6 months prior to treatment on this protocol will be acceptable
* NOTE: Arms A/B - relapsed or refractory DLBCL within 24 months from the end of anthracycline-based therapy; no prior salvage therapy; patients can have received radiation therapy as part of initial treatment but not specifically for relapse
* NOTE: Arm C patients include relapsed or refractory lymphoma patients of any type for which the recommended treatment includes one of the platinum-based regimens; of note, relapsed or refractory double-hit high grade lymphoma patients and relapsed or refractory Hodgkin lymphoma patients will be enrolled in Arm C; there is no limit on the number of prior therapies for Arm C patients; the patient must be eligible for a platinum-based regimen and must not have received the same regimen in the past without responding
* Measurable or assessable disease: measurable disease is defined as measurable by computed tomography (CT) \[dedicated CT or the CT portion of a positron emission tomography (PET)/CT\] or magnetic resonance imaging (MRI): to be considered measurable, there must be at least one lesion that has a single diameter of \>= 1.5 cm
* NOTE: Skin lesions can be used if the area is \>= 1.5 cm in at least one diameter and photographed with a ruler; patients with assessable disease by PET are also eligible as long as the assessable disease is biopsy proven lymphoma
* Arms A/B - eligible for treatment with ifosfamide, carboplatin, and etoposide (+/- rituximab)
* Arm C eligible for treatment with one of the following standard, every 3 week, platinum-based salvage regimens (with or without monoclonal antibody as appropriate for the disease):
* Ifosfamide/carboplatin/etoposide (ICE) or rituximab/ifosfamide/carboplatin/etoposide (RICE);
* Cisplatin, cytarabine (cytosine arabinoside), dexamethasone (DHAP) or RDHAP;
* Gemcitabine hydrochloride (gemcitabine), dexamethasone, cisplatin (GDP) or rituximab, gemcitabine, dexamethasone, cisplatin (RGDP);
* Gemcitabine and oxaliplatin (GemOx) or rituximab, gemcitabine and oxaliplatin (RGemOx);
* Oxaliplatin, cytosine arabinoside, dexamethasone (OAD) or rituximab, oxaliplatin, cytosine arabinoside, dexamethasone (ROAD)
* Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1 or 2
* Hemoglobin \>= 8.0 g/dL (may transfuse to meet this requirement), obtained =\< 14 days prior to registration
* Absolute neutrophil count (ANC) \>= 1500/mm\^3, obtained =\< 14 days prior to registration
* Platelet count \>= 75000/mm\^3, obtained =\< 14 days prior to registration
* Total bilirubin =\< 2 x upper limit of normal (ULN) (if \> 2 x ULN direct bilirubin is required and should be =\< 1.5 x ULN), obtained =\< 14 days prior to registration
* Alanine aminotransferase (ALT) and aspartate transaminase (AST) =\< 3 x ULN (=\< 5 x ULN for patients with liver involvement), obtained =\< 14 days prior to registration
* Creatinine =\< 1.6 mg/dL; if over 1.6 then the calculated creatinine clearance must be \>= 55 ml/min using the Cockcroft-Gault formula, obtained =\< 7 days prior to registration
* Negative pregnancy test done =\< 7 days prior to registration, for persons of childbearing potential only
* NOTE: If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required
* Human immunodeficiency virus (HIV) test done =\< 14 days prior to registration
* If positive, the CD4 count must be \> 400
* Provide written informed consent
* Willingness to have a central venous line \[peripherally inserted central catheter (PICC) or PORT\]
* Willingness to provide mandatory blood specimens for correlative research
* Willingness to provide mandatory tissue specimens for correlative research
* Willingness to return to enrolling institution for follow-up (during the active monitoring phase of the study)
* Willingness to follow the requirements of the intravenous ascorbic acid program schedule
* ARM D: Patients who had a diagnosis of CCUS with one or more TET2 mutations or TET2 mutations with concurrent splicing genes mutations (SRSF2, U2AF1, SF3B1, and ZRSR2) or epigenetic regulator mutations (DNMT3A, EZH2, IDH1, IDH2). CCUS diagnosis being defined based on the absence of definitive morphologic evidence of hematologic neoplasms from bone marrow biopsy evaluation combined with evidence of pathogenic myeloid somatic mutation with a variant allele frequency (VAF) of at least 2% using our institution's next generation sequencing (NGS) panel (OncoHeme, Mayo Clinic)
* ARM D: ECOG performance status (PS) 0, 1 or 2
* ARM D: Patients must meet at least 1 of these 3 laboratory criteria to be enrolled:
* Hemoglobin =\< 10g/dL (obtained =\< 7 days prior to registration)
* Absolute neutrophil count (ANC) =\< 1000/mm\^3 (obtained =\< 7 days prior to registration)
* Platelet count =\< 100,000/mm\^ 3 (obtained =\< 7 days prior to registration)
* ARM D: Total bilirubin =\< 2 x ULN (if \> 2 x ULN direct bilirubin is required and should be =\< 1.5 x ULN) (obtained =\<7 days prior to registration)
* ARM D: Alanine aminotransferase (ALT) and aspartate transaminase (AST) =\< 3 x ULN (=\< 5 x ULN for patients with liver involvement) (obtained =\<7 days prior to registration)
* ARM D: Creatinine =\< 1.6 mg/dL (obtained =\<7 days prior to registration). If \> 1.6, then the Calculated creatinine clearance must be \>= 55 ml/min using the Cockcroft-Gault formula
* ARM D: Negative pregnancy test, for persons of childbearing potential only (obtained =\< 7 days prior to registration). NOTE: If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required.
* ARM D: Provide written informed consent
* ARM D: Willingness to have a central venous line (PICC or PORT)
* ARM D: Willingness to provide mandatory blood specimens for correlative research
* ARM D: Willingness to return to enrolling institution (MCR) for follow-up (during the active monitoring phase of the study)
* ARM D: Willingness to follow the requirements of the intravenous ascorbic acid program schedule
* ARM E PRE-REGISTRATION: Age ≥ 18 years
* ARM E PRE-REGISTRATION: New or an established diagnosis of 2016 World Health Organization (WHO) defined chronic myelomonocytic leukemia with a somatic TET2, IDH1, or IDH2 mutation requiring treatment with DNA methyltransferase inhibitors/hypomethylating agents
* ARM E PRE-REGISTRATION: No prior CMML directed therapy.
* Exception: Received ≤ 1 cycle of azacitidine, decitabine, erythropoiesis stimulating agent therapy (ESA), or oral decitabine and cedazuridine. NOTE: Prior exposure to hydroxyurea is allowed. Continuation beyond the first cycle must be discussed with the principal investigator (PI)
* ARM E PRE-REGISTRATION: Creatinine ≤ 1.6 mg/dL. If \> 1.6, then the Calculated creatinine clearance must be ≥ 55 ml/min using the Cockcroft-Gault formula
* ARM E PRE-REGISTRATION: Willingness to provide mandatory research bone marrow sample for correlative research
* ARM E PRE-REGISTRATION: ECOG performance status (PS) 0, 1, or 2
* ARM E PRE-REGISTRATION: Provide written informed consent
* ARM E REGISTRATION: Willingness to provide mandatory blood specimens for correlative research
* ARM E REGISTRATION: Willingness to return to enrolling institution (MCR) for follow-up (during the active monitoring phase of the study)
* ARM E REGISTRATION: Recovered to grade 1 or baseline or established as sequelae from all toxic effects of previous therapy except alopecia
* ARM E REGISTRATION: Absolute neutrophil count (ANC) ≥ 500/mm\^3 (obtained ≤ 7 days prior to registration)
* ARM E REGISTRATION: Platelet count ≥ 20,000/mm\^3 (obtained ≤ 7 days prior to registration)
* ARM E REGISTRATION: Total bilirubin ≤ 1.5 x ULN ( ≤ 3 x ULN for patients with Gilbert's syndrome) (obtained ≤ 7 days prior to registration)
* ARM E REGISTRATION: Alanine aminotransferase (ALT) and aspartate transaminase (AST) ≤ 3 x ULN (obtained ≤ 7 days prior to registration)
* ARM E REGISTRATION: Ability to complete questionnaire by themselves or with assistance
* ARM E REGISTRATION: For a person of child-bearing potential (WOCBP): Must agree to use contraception or take measures to avoid pregnancy during the study. Adequate contraception is defined as follows:
* Complete true abstinence
* Consistent and correct use of one of the following methods of birth control:
* Male partner who is sterile prior to the female patient's entry into the study and is the sole sexual partner for that female patient
* Implants of levonorgestrel
* Injectable progestogen
* Intrauterine device (IUD) with a documented failure rate of less than 1% per year
* Oral contraceptive pill (either combined or progesterone only)
* Barrier method, for example: diaphragm with spermicide or condom with spermicide in combination with either implants of levonorgestrel or injectable progestogen
* ARM E REGISTRATION: WOCBP must have a negative serum or urine pregnancy test ≤ 7 days prior to registration. NOTE: WOCBP include any person who has experienced menarche and who has not undergone successful surgical sterilization (hysterectomy, bilateral tubal ligation, or bilateral oophorectomy) or is not postmenopausal (defined as amenorrhea \> 12 consecutive months); or women on hormone replacement therapy with documented serum follicle stimulating hormone (FSH) level \> 35 mIU/mL. Even women who are using oral, implanted, or injectable contraceptive hormones or mechanical products such as an IUD or barrier methods (diaphragm, condoms, spermicides) to prevent pregnancy or practicing abstinence or where partner is sterile (e.g., vasectomy), must be considered to be of child-bearing potential. NOTE: If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required
* ARM E REGISTRATION: Persons who are able to father a child must use contraception during the study and for 3 months after the last treatment dose.
* Complete true abstinence
* Latex condom with a spermicidal agent
* Diaphragm with spermicide
* ARM E REGISTRATION: Willingness to have a central venous line (PICC or PORT)
* ARM E REGISTRATION: Willingness to follow the requirements of the intravenous ascorbic acid program schedule
Exclusion Criteria:
* Any of the following:
* Pregnant persons
* Nursing persons
* Persons of childbearing potential who are unwilling to employ adequate contraception
* Any therapy =\< 2 weeks prior to registration; NOTE: Exception: patients on ibrutinib or corticosteroids (any dose) may continue therapy up until the new regimen has started at investigator discretion; corticosteroids can be tapered to lowest possible dose after start of treatment at investigator discretion. Exception: Palliative radiation is allowed
* Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, pulmonary congestion or pulmonary edema, clinical dehydration, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
* Receiving any other investigational agent which would be considered as a treatment for the lymphoma
* Other active malignancy than lymphoma
* NOTE: If there is a history of prior malignancy, they must not be receiving other specific treatment for their cancer that could interfere with this protocol therapy; patients on hormonal therapy for treated breast or prostate cancer are permitted if they meet other eligibility criteria; patients with non-melanotic skin cancer may enroll
* History of myocardial infarction =\< 6 months, or current symptomatic congestive heart failure or left ventricular ejection fraction (LVEF) \< 40% or with \> grade 2 diastolic dysfunction, with no symptoms or signs of heart failure
* Known G6PD (glucose-6-phosphate dehydrogenase) deficiency (below lower limit of normal)
* Patients with active central nervous system (CNS) lymphoma or active cerebrospinal fluid (CSF) involvement with malignant cells requiring CNS-specific therapy with IV or intrathecal (IT) methotrexate (MTX); Note: Patients with any prior CNS lymphoma (parenchymal or leptomeningeal) MUST be in complete remission (CR) in those compartments without any maintenance therapy required
* Patients with uncontrolled or symptomatic kidney stones
* Known paroxysmal nocturnal hemoglobinuria (PNH)
* ARM D: Bona-fide hematological neoplasm
* ARM D: Any of the following because this study involves an agent that has known genotoxic, mutagenic and teratogenic effects:
* Pregnant persons
* Nursing persons
* Persons of childbearing potential who are unwilling to employ adequate contraception
* ARM D: Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens
* ARM D: Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, pulmonary congestion or pulmonary edema, clinical dehydration, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
* ARM D: History of myocardial infarction =\< 6 months, or current symptomatic congestive heart failure or known LVEF \< 40% or with \> grade 2 diastolic dysfunction, with no symptoms or signs of heart failure
* ARM D: Patients with uncontrolled or symptomatic kidney stones
* ARM D: Known paroxysmal nocturnal hemoglobinuria (PNH)
* ARM D: Known G6PD (glucose-6-phosphate dehydrogenase) deficiency (below lower limit of normal)
* ARM E PRE-REGISTRATION: Myelodysplastic syndrome (MDS)/myeloproliferative neoplasm (MPN) overlap syndromes other than CMML
* ARM E PRE-REGISTRATION: Active central nervous system disease
* ARM E PRE-REGISTRATION: Any active disease condition that would render the protocol treatment dangerous or impair the ability of the patient to receive study drug
* ARM E PRE-REGISTRATION: Concurrent active malignancy, except adequately treated nonmelanoma skin cancer. History of curatively treated in situ cancer of the cervix, curatively treated in situ cancer of the breast, or other solid tumors curatively treated is allowed as long as there is no evidence of disease for \> 2 years
* ARM E PRE-REGISTRATION: Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens
* ARM E PRE-REGISTRATION: Disease requiring systemic treatment with systemic immunosuppression with steroid steroids at a dose of ≥ 20 mg/day prednisone (or equivalent). Exceptions: Intermittent use of bronchodilators or inhaled steroids, local steroid injections, topical steroids
* ARM E PRE-REGISTRATION: Patients with uncontrolled or symptomatic kidney stones
* ARM E REGISTRATION: New York Heart Association (NYHA) class III/IV heart failure or active angina/angina equivalents
* ARM E REGISTRATION: History of myocardial infarction ≤ 6 months, or current symptomatic congestive heart failure or known LVEF \< 40% or with \> grade 2 diastolic dysfunction, with no symptoms or signs of heart failure
* ARM E REGISTRATION: Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, clinically significant cardiac arrhythmia, unstable angina pectoris, clinically significant nonhealing or healing wounds, pulmonary congestion or pulmonary edema, significant pulmonary disease (shortness of breath at rest or mild exertion), uncontrolled infection, clinical dehydration, or psychiatric illness/social situations that would limit compliance with study requirements
* ARM E REGISTRATION: Known G6PD (glucose-6-phosphate dehydrogenase) deficiency (below lower limit of normal)
* ARM E REGISTRATION: Any of the following because this study involves an agent that has known genotoxic, mutagenic, and teratogenic effects:
* Pregnant persons
* Nursing persons
* Persons of childbearing potential who are unwilling to employ adequate contraception
