Patients with known human immunodeficiency virus (HIV) must have a CD4 count > 350 and be on concurrent antiretrovirals; patients with a history of intravenous drug abuse or any behavior associated with an increased risk of HIV infection should be tested for exposure to the HIV virus; an HIV test is not required for entry on this protocol, but is required if the patient is perceived to be at risk Patients must not have any known immune deficiencies; patients with immune deficiency are at increased risk of lethal infections when treated with marrow-suppressive therapy; therefore, known human immunodeficiency virus (HIV) positive patients receiving combination anti-retroviral therapy are excluded from the study Patients with human immunodeficiency virus (HIV) who are not receiving cytochrome p450 inhibitors, and who have a minimum of 300+ CD4+ cells/mm^3, an undetectable viral load, and no history of acquired immune deficiency syndrome (AIDS) indicator conditions HIV-positive patients on combination antiretroviral therapy which include cytochrome p450 inhibitors are ineligible; patients with CD4 counts less than 300 CD4+ cells/mm^3 and or a high viral load are ineligible Human immunodeficiency virus (HIV) positive with CD4 count < (350) cells/microliter; note that patients who are HIV positive are eligible, provided they are under treatment with highly active antiretroviral therapy (HAART) and have a CD4 count >= (350) cells/microliter, and no known detectable viral load, at the time of study entry; note also that HIV testing is not required for eligibility for this protocol Human immunodeficiency virus (HIV) positive patients are allowed on this study if they have a CD4 count > 400, and are on a stable antiviral regimen; patients with poorly controlled HIV or other chronic active viral infections will be excluded RANDOMIZED PHASE II (ARMS K AND L): HIV positive patients are eligible provided they meet the other protocol criteria including the following:* Long term survival expected were it not for the cHL* HIV viral loads undetectable by standard clinical HIV testing* Willing to adhere to effective combination antiretroviral therapy Patients who are known to be human immunodeficiency virus positive (HIV+) are eligible providing they meet all of the following additional criteria within 28 days prior to registration:* CD4+ cells >= 350/mm^3 (nadir)* Viral load of < 50 copies HIV messenger ribonucleic acid (mRNA)/mm^3 if on combination antiretroviral therapy (cART) or < 25,000 copies HIV mRNA if not on cART* No zidovudine or stavudine as part of cARTPatients who are HIV+ and do not meet all of these criteria are not eligible for this study Human immunodeficiency virus (HIV) positive patients who are not on retroviral therapy will not be excluded from cohort 1, the normal liver function cohort* HIV positive patients who are not on retroviral therapy will be excluded from cohorts 2-4 Human immunodeficiency virus (HIV)-positive patients on highly active antiretroviral therapy (HAART) are excluded Patients known to be positive for HIV (the human immunodeficiency virus) may be eligible, providing they meet the following additional criteria within 28 days prior to registration:* No history of acquired immune deficiency syndrome (AIDS)-defining conditions* CD4 cells > 350 cells/mm^3* If on antiretroviral agents, must not include zidovudine or stavudine* Viral load =< 50 copies HIV messenger ribonucleic acid (mRNA)/mm^3 if on combination antiretroviral therapy (cART) or =< 25,000 copies HIV mRNA/mm^3 if not on cART* Highly active antiretroviral therapy (HAART) regimens are acceptable providing they have only weak P450A4 interactions Human immunodeficiency virus (HIV) positive with cluster of differentiation (CD)4 count < 200 cells/microliter; note that patients who are HIV positive are eligible, provided they are under treatment with highly active antiretroviral therapy (HAART) and have a CD4 count >= 200 cells/microliter within 30 days prior to registration; note also that HIV testing is not required for eligibility for this protocol Patients with known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS) might be enrolled if the viral load by PCR is undetectable with/without active treatment and absolute lymphocyte count >= 350/ul Human immunodeficiency virus (HIV) infected patients are eligible provided they meet all other eligibility criteria, and:* There is no prior history of acquired immunodeficiency syndrome (AIDS) defining conditions other than historically low CD4+ T-cell count or B-cell lymphoma* In the opinion of an expert in HIV disease, prospects for long-term survival are excellent were it not for the diagnosis of lymphoma* Use of HIV protease inhibitors as part of the anti-HIV regimen OR as a pharmacologic booster is not allowed* Zidovudine is not allowed* Once daily combination pills for HIV containing a pharmacologic booster such as cobicistat are not allowed* Patients with multi-drug resistant HIV are not eligible Patients who are human immunodeficiency virus (HIV) positive on highly active anti-retroviral therapy (HAART) will be excluded from the study Human immunodeficiency virus (HIV) infected patients (if HIV positive)* HIV infected individuals are eligible provided they meet all the protocol eligibility criteria in addition to the following:** No history of acquired immune deficiency syndrome (AIDS) defining illness other than a historic CD4+ T-cell nadir < 200/mm^3** Prior to leukemia diagnosis, the HIV disease was uncomplicated as evidenced by:*** The CD4+ T-cell counts were generally in excess of 300/mm^3*** The HIV viral loads were less than 200 copies/ml if on anti-HIV therapy*** If the HIV is newly diagnosed or there is no history of using anti-HIV therapy, there are no AIDS defining conditions or other HIV-related symptoms*** Zidovudine is not allowed as part of the anti-HIV therapy Human immunodeficiency virus (HIV) infected patients are eligible provided they meet all the other eligibility criteria of the study in addition to the following: * No history of acquired immune deficiency syndrome (AIDS)-defining conditions other than lymphoma or history of CD4+ T-cells below 200/mm^3 prior to beginning combination antiretroviral therapy (cART)* After HIV diagnosis and during treatment with cART, patients should have maintained CD4+ T-cells >= 350/mm^3 prior to lymphoma diagnosis; patients who never immune reconstituted to a stable level above 350/mm^3 are not eligible* At time of study entry CD4+ T-cells must have recovered from prior lymphoma therapy to >= 250/mm^3* At the time of study entry the HIV viral load must be undetectable by standard laboratory assay * During prior lymphoma therapy, patients must not have experienced documented infections attributed to the HIV+ status* No history of non-adherence to cART and willing to adhere to cART while on study* Antiretroviral drugs with overlapping or similar toxicity profiles as study agents not allowed:** Efavirenz not allowed** Stavudine not allowed** Zidovudine not allowed* Patients must be willing to be followed at a minimum of approximately every 3 months by physician expert in HIV disease management Human immunodeficiency virus (HIV)-positive patients with well-controlled disease, as determined by CD4 count and viral load, who are on antiretroviral therapy that does not contain a strong inducer or inhibitor of CYP3A4 are allowed on trial; HIV-positive patients on combination antiretroviral therapy with strong inducers or inhibitors of CYP3A4 are ineligible; patients with poorly controlled HIV are not eligible Human immunodeficiency virus (HIV)+ patients are eligible for the trial provided they meet the other study criteria in addition to the following:* CD4+ T-cells >= 250/mm^3* HIV sensitive to antiretroviral therapy* Zidovudine not allowed* Long term survival anticipated on the basis of HIV alone were it not for the lymphoma* No concurrent acquired immunodeficiency syndrome (AIDS)-defining illness other than the lymphoma Healthy human immunodeficiency virus (HIV)-infected patients are eligible, provided that they meet all the other study criteria in addition to the following (HIV testing is not required for study enrollment):* CD4+ cell count >= 250/mm^3* HIV viral loads undetectable by standard clinical tests Human immunodeficiency virus (HIV)-positive patients with well-controlled disease, as determined by CD4 count and viral load, who are on antiretroviral therapy that does not contain a strong inducer or inhibitor of CYP3A4 (e.g. regimens containing ritonavir, cobicistat, efavirenz or etravirine) are allowed on trial; HIV-positive patients on combination antiretroviral therapy with strong inducers or inhibitors of CYP3A4 are ineligible; patients with poorly controlled HIV are not eligible Patients with concurrent human immunodeficiency virus (HIV) infection may be enrolled if compliant with 3 or more drug anti-retroviral regimen and virus load less than 50 copies/ml and CD4 count greater than 250 cells/ml, and no concurrent opportunistic infection or other malignancy Patients known to be human immunodeficiency virus (HIV) positive are eligible if they meet the following criteria within 30 days prior to registration: stable and adequate CD4 counts (>= 350 mm^3), and serum HIV viral load of < 25,000 IU/ml; patients must be on a stable anti-viral therapy Human immunodeficiency virus (HIV)-positive patients are eligible provided the following criteria are met: CD4 count > 350/mm^3, an undetectable viral load, and not receiving prophylaxis antibiotics Known human immunodeficiency virus (HIV) positive with CD4 count < 200 cells/microliter. Note that patients who are HIV positive are eligible, provided they are under treatment with highly active antiretroviral therapy (HAART) and have a CD4 count >= 200 cells/microliter within 30 days prior to registration; note also that HIV testing is not required for eligibility for this protocol; this exclusion criterion is necessary because the treatments involved in this protocol may be significantly immunosuppressive. Human immunodeficiency virus (HIV) positive with cluster of differentiation 4 (CD4) count < 200 cells/microliter; note that patients who are HIV positive are eligible, provided they are under treatment with highly active antiretroviral therapy (HAART) and have a CD4 count >= 200 cells/microliter within 30 days prior to step 1 registration; note also that HIV testing is not required for eligibility for this protocol Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible; patients must also have a CD4 count > 350 cells/mm^3 with an undetectable viral load Patients positive for human immunodeficiency virus (HIV) are NOT excluded from this study, but HIV-positive patients must have:* A stable regimen of highly active anti-retroviral therapy (HAART)* No requirement for concurrent antibiotics or antifungal agents for the prevention of opportunistic infections* A cluster of differentiation (CD)4 count above 250 cells/mcL and an undetectable HIV viral load on standard PCR-based tests Patients positive for human immunodeficiency virus (HIV) are eligible only if they have all of the following:* A stable regimen of highly active anti-retroviral therapy (HAART)* No requirement for concurrent antibiotics or antifungal agents for the prevention of opportunistic infections* A CD4 count above 250 cells/mcL and an undetectable HIV viral load on standard PCR-based tests Patients positive for human immunodeficiency virus (HIV) are NOT excluded from this study, but HIV-positive patients must have:* A stable regimen of highly active anti-retroviral therapy (HAART)* No requirement for concurrent antibiotics or antifungal agents for the prevention of opportunistic infections* A CD4 count above 250 cells/mcL and an undetectable HIV viral load on standard polymerase chain reaction (PCR)-based test Patients who have previously tested positive for human immunodeficiency virus (HIV) are NOT excluded from this study (please note: testing of all patients wishing to enroll is NOT required), but HIV-positive patients must have:* A stable regimen of highly active anti-retroviral therapy (HAART)* No requirement for concurrent antibiotics or antifungal agents for the prevention of opportunistic infections* A CD4 count above 250 cells/mcL and an undetectable HIV viral load on standard PCR-based tests Patients with a known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS) will be eligible if:* They are generally healthy from an HIV perspective and on a stable anti-retroviral regimen for > 6 months* They have had no AIDS-defining conditions in the past 12 months other than historically low CD4+ cell counts* They have an undetectable viral load on standard assays Patients positive for human immunodeficiency virus (HIV) are NOT excluded from this study, but HIV-positive patients must have:* A stable regimen of highly active anti-retroviral therapy (HAART)* No requirement for concurrent antibiotics or antifungal agents for the prevention of opportunistic infections* A CD4 count above 250 cells/mcL and an undetectable HIV viral load on standard PCR-based tests Patients with known active human immunodeficiency virus (HIV) infection; patients with chronic HIV with a CD4 > 250, undetectable viral load by PCR, without opportunistic infection, and on a stable regimen of highly active anti-retroviral therapy (HAART) therapy would be eligible Human immunodeficiency virus (HIV) positive patients are not excluded, but to enroll, must meet all of the below criteria:* HIV is sensitive to antiretroviral therapy* Must be willing to take effective antiretroviral therapy that has minimal overlapping toxicity and pharmacokinetic interactions with protocol therapy* No history of HIV-related opportunistic disease or acquired immune deficiency syndrome (AIDS)-defining conditions within past 12 months other than historic CD4+ T-cell counts below 200 cells/mm^3* Expected long-term survival if lymphoma were not present Patients positive for human immunodeficiency virus (HIV) are eligible only if they meet all of the following:* A stable regimen of highly active anti-retroviral therapy (HAART)* No requirement for concurrent antibiotics or antifungal agents for the prevention of opportunistic infections* A CD4 count above 250 cells/mcL, and an undetectable HIV viral load on standard PCR-based tests Patients positive for human immunodeficiency virus (HIV) are NOT excluded from this study, but HIV-positive patients must have:* A stable regimen of highly active anti-retroviral therapy (HAART)* No requirement for concurrent antibiotics or antifungal agents for the prevention of opportunistic infections* A CD4 count above 250 cells/mcL and an undetectable HIV viral load on standard PCR-based tests Patients who are human immunodeficiency virus (HIV) positive may participate IF they meet the following eligibility requirements:* They must be stable on their anti-retroviral regimen, and they must be healthy from an HIV perspective* They must have a CD4 count of greater than 250 cells/mcL* They must not be receiving prophylactic therapy for an opportunistic infection Human immunodeficiency virus (HIV) positive (+) patients with CD4 counts >= 250 cells/mm^3 on anti-viral therapy are eligible for the study HIV positive with CD4 count < 200 cells/microliter; note that patients who are human immunodeficiency virus (HIV) positive are eligible, provided they are under treatment with highly active antiretroviral therapy (HAART) and have a CD4 count >= 200 cells/microliter prior to registration; note also that HIV testing is not required for eligibility for this protocol Human immunodeficiency virus (HIV)-patients positive for human immunodeficiency virus (HIV) are NOT excluded from this study, however HIV-positive patients must meet the following criteria:* A stable regimen of highly active anti-retroviral therapy (HAART)* No requirement for concurrent antibiotics or antifungal agents for the prevention of opportunistic infections* A CD4 count above 250 cells/mcL and an undetectable HIV viral load on standard polymerase chain reaction (PCR)-based test Patients positive for human immunodeficiency virus (HIV) are NOT excluded from this study, but HIV-positive patients must have:* A stable regimen of highly active anti-retroviral therapy (HAART)* No requirement for concurrent antibiotics or antifungal agents for the prevention of opportunistic infections* A CD4 count above 250 cells/mcL and an undetectable HIV viral load on standard PCR-based tests