Ofatumumab in Combination With Cyclophosphamide, Doxorubicin Hydrochloride, Vincristine Sulfate, and Dexamethasone Alternating With Ofatumumab in Combination With Cytarabine and Methotrexate in Treating Patients With Newly Diagnosed Mantle Cell Lymphoma

Inclusion Criteria:

* Histologically documented mantle cell lymphoma with co-expression of CD20 and CD5 and lack of CD23 expression by immunophenotyping and at least one of the following confirmatory tests: 1) positive immunostaining for cyclin D1; 2) the presence of t(11;14) on cytogenetic analysis; OR 3) molecular evidence of B-cell leukemia/lymphoma 1 (bcl-1)/immunoglobulin heavy locus (IgH) rearrangement

  * Cases that are CD5-negative and/or CD23-positive will be eligible provided that the histopathology is consistent with mantle cell lymphoma AND positive for cyclin D1, t(11;14), or bcl-1/IgH rearrangement
  * A tissue block or unstained slides (10 - 20 slides) will be submitted to the Roswell Park Cancer Institute (RPCI) Pathology Department for central pathology review
  * A diagnosis based on peripheral blood or bone marrow aspirate is allowed; if the diagnosis is based only on blood, in addition to the immunophenotype and molecular confirmation above, a peripheral blood smear must be available for central pathology review; if the diagnosis is based on a bone marrow, the bone marrow core biopsy or aspirate clot tissue block will be submitted to the RPCI Pathology Department: if the tissue block is not available please submit the diagnostic smears for review
* Extent of disease: stage I - IV; patients with nodular histology mantle cell lymphoma must have Ann Arbor stage III or IV disease to be eligible

  * Patients with mantle zone type histology will not be eligible
  * Patients with other mantle cell histologies are eligible regardless of stage
* Measurable or assessable disease is required; measurable tumor size (at least one node measuring 2.25 cm\^2 in bidimensional measurement)
* No active central nervous system (CNS) disease defined as symptomatic meningeal lymphoma or known CNS parenchymal lymphoma; a lumbar puncture demonstrating mantle cell lymphoma at the time of registration to this study is not an exclusion for study enrollment
* Patients must be previously untreated
* No prior radiation therapy for mantle cell lymphoma
* \>= 2 weeks since major surgery
* No known hypersensitivity to murine products
* No medical condition requiring chronic use of high dose systemic corticosteroids (i.e., doses of prednisone higher than 10 mg/day or equivalent)
* No human immunodeficiency virus (HIV) infection; 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; patients who test positive or who are known to be infected are not eligible; an HIV test is not required for entry on this protocol, but is required if the patient is perceived to be at risk
* Non-pregnant and non-nursing; women and men of reproductive potential should agree to use an effective means of birth control
* Patients who test positive for hepatitis C antibody (Ab) are eligible provided all of the following criteria are met: 1) total bilirubin =\< 2 x upper limit of normal; 2) AND aspartate aminotransferase (AST) =\< 3 x upper limit of normal; AND 3) liver biopsy (pathology) demonstrates =\< grade 2 fibrosis and no cirrhosis
* Specific guidelines will be followed regarding inclusion of MCL based on hepatitis B serological testing as follows:

  * Hepatitis B surface antigen (HBsAg) negative, hepatitis B core antibody (HBcAb) negative, hepatitis B surface antibody (HBsAb) positive MCL patients are eligible
  * Patients who test positive for HBsAg are ineligible (regardless of other hepatitis B serologies)
  * For MCL patients with HBsAg negative, but HBcAb positive (regardless of HBsAb status), should have hepatitis B virus (HBV) deoxyribonucleic acid (DNA) testing done and protocol eligibility determined as follows:

    * If HBV DNA is positive the subject is excluded
    * If HBV DNA is negative, patient may be included but must undergo at least every 2 months HBV DNA polymerase chain reaction (PCR) testing from the start of treatment throughout the duration the study
    * Monitoring during the study is required at least every 2 months and during follow-up at a minimum of every 2-3 months up to 6 months after the last dose
    * Prophylactic antiviral therapy with lamivudine (3TC) or investigator's preferred antiviral regimen throughout protocol therapy and for 6-12 months thereafter may be initiated at the discretion of the investigator
    * If the patients' HBV DNA becomes positive during the study, the investigator should manage the clinical situation as per the standard of care of participating institution; the investigator should weigh the risks and benefits of continuing ofatumumab or discontinuing ofatumumab before appropriate treatment decisions are made for that individual patient
* Patients must not have a history of cardiac disease, defined as New York Heart Association class II or greater or clinical evidence of congestive heart failure (CHF)
* No known hypersensitivity to ofatumumab, humanized antibodies or chemotherapy agents throughout the protocol
* Left ventricular ejection fraction (LVEF) by multi gated acquisition scan (MUGA) or echocardiogram (ECHO) \>= 45%
* Neutrophils \> 1000/uL
* Platelets \>= 75,000/uL (unless significant bone marrow involvement with MCL)
* Creatinine =\< 2.0 mg/dL
* Total bilirubin =\< 2.0 mg/dL (unless MCL related or attributable to Gilbert's disease)
* Urine or serum beta-human chorionic gonadotropin (HCG) or serum HCG = negative (if female patient of childbearing potential)
* Patient or legal representative must understand the investigational nature of this study and sign an Independent Ethics Committee/Institutional Review Board approved written informed consent form prior to receiving any study related procedure
* Consult with a physician experience in care and management of subjects with hepatitis B to manage/treat subjects who are anti-hepatitis B core antibody (HBc) positive

Exclusion Criteria:

* Prior history of HIV-positivity (routine HIV testing is not required pre-treatment)
* Positive serology for hepatitis B (HB) defined as a positive test for HBsAg; in addition, if negative for HBsAg but HBcAb positive (regardless of HBsAb status), a hepatitis B DNA test will be performed and if positive the patient will be excluded
* Serious non-malignant disease (e.g., active uncontrolled bacterial, viral, or fungal infections) or other medical conditions (including psychiatric) which, in the opinion of the Principal Investigator (PI) would compromise other protocol objectives
* Presence of symptomatic CNS lymphoma
* Pregnant or lactating females
* Prior history of radiation or chemotherapy for MCL
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to ofatumumab or other agents used in study
* Patients with a "currently active" second malignancy, other than non-melanoma skin cancer or in situ carcinoma of the cervix or breast; patients are not considered to have a "currently active" malignancy if they have completed anti-cancer therapy, are considered by their physician to be at less than 30% risk of relapse and at least 2-5 years have lapsed
* Major surgery, other than diagnostic surgery, within 2 weeks
* Patients with non-Hodgkin lymphoma (NHL) other than MCL
* Patients must not have a history of cardiac disease, defined as New York Heart Association class II or greater or clinical evidence of congestive heart failure; all patients must have a MUGA scan or 2-dimensional (D) echocardiogram indicating an ejection fraction of \>= 45% within 42 days prior to registration; the method used at baseline must be used for later monitoring
* Unwilling or unable to follow protocol requirements
* Any condition which in the Investigator's opinion deems the patient an unsuitable candidate to receive study drug
* Received an investigational agent within 30 days prior to enrollment