Ofatumumab and Bortezomib in Subjects With Relapsed CD20+Diffuse Large B Cell, Follicular, or Mantle Cell Lymphoma

Inclusion Criteria: * Patients must have biopsy sample obtained within 6 months of study entry that: * Is histologically confirmed DLBCL, MCL or FL, by an Oregon Health and Science University (OHSU) hematopathologist * Retains expression of CD20+ * Patients must be refractory to or have recurrent disease after prior rituximab containing treatment; relapse or progression is defined according the International Working Group (IWG) response criteria * FL patients must have disease-related symptoms, cytopenias, threatened end-organ function, bulky or progressive disease, or it is the patient's preference to be treated * DLBCL and MCL patients must be either transplant ineligible or have refused high dose therapy * Patients must have radiographically measurable disease, as defined by the IWG criteria; the same method of assessment used to measure each lesion at baseline must be used for all subsequent tumor measurements throughout the study * There is no limit to the number of prior treatments * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Absolute neutrophil count \>= 1.0 K/mm\^3 * Platelets \>= 50 K /mm\^3 * Total bilirubin =\< 1.5 x normal institutional limits, unless secondary to Gilbert's disease * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase (SGOT))/alanine aminotransferase (ALT) (serum glutamic pyruvate transaminase (SGPT)) =\< 2.5 x institutional upper limit of normal (ULN) * Alkaline Phosphatase \< 2.5 times ULN (unless due to disease involvement of the liver or bone marrow) * Patients must be able to comply with study procedures and follow-up examinations * Women of childbearing potential (not surgically sterile or \< 12 months naturally post-menopausal) must be willing to use medically accepted method of contraception for the duration and 6 months following the end of the treatment; acceptable methods of contraception include abstinence, barrier method with spermicidal or hormonal contraceptive (oral, transdermal, implanted and injected) in conjunction with a barrier method * Men who are not surgically sterile must practice abstinence or use a barrier method of birth control for the duration and 6 months following the end of treatment * Patients must have the ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Subjects who have current active hepatic or biliary disease (with the exception of patients with Gilbert's syndrome, asymptomatic gallstones, liver metastases or stable chronic liver disease per investigator assessment) * Patients who have had chemotherapy, antibody or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C); corticosteroids for symptom control are allowed up to 7 days of starting protocol treatment * Patients may not have received any other investigational agents within 4 weeks, or may not be currently participating in any other interventional clinical study * Prior treatment with ofatumumab or bortezomib * Prior treatment with anti-CD20 monoclonal antibody or alemtuzumab within 3 months prior to start of therapy * Diagnosis of another malignancy, unless the patient has been disease-free or at least 5 years following the completion of curative intent therapy with the following exceptions: patients with treated non-melanoma skin cancer, in situ carcinoma, or cervical intraepithelial neoplasia, regardless of the disease-free duration, are eligible for this study if definitive treatment for the condition has been completed; patients with organ-confined prostate cancer with no evidence of recurrent or progressive disease based on prostate-specific antigen (PSA) values are also eligible for this study if hormonal therapy has been initiated or a radical prostatectomy has been performed * History of allergic reactions attributed to compounds of similar chemical or biologic composition to ofatumumab or bortezomib * Peripheral neuropathy or neuropathic pain of Grade 2 or greater * Chronic or current infectious disease requiring systemic antibiotics, antifungal, or anti-viral treatment such as, but not limited to, chronic renal infection, chronic chest infection with bronchiectasis and tuberculosis * History of significant cerebrovascular disease in the past 6 months or ongoing event with active symptoms or sequelae * Clinically significant cardiac disease including unstable angina, acute myocardial infarction within six months prior to randomization, congestive heart failure (New York Heart Association (NYHA) III-IV), and arrhythmia unless controlled by therapy, with the exception of extra systoles or minor conduction abnormalities * Significant concurrent, uncontrolled medical condition including, but not limited to, renal, hepatic, gastrointestinal, endocrine, pulmonary, neurological, cerebral or psychiatric disease which in the opinion of the investigator may represent a risk for the patient * Pregnant or breast feeding women * Known human immunodeficiency virus (HIV) infection * Positive serology for Hepatitis B (HB) defined as a positive test for HB surface antigen (HBsAg); in addition, if negative for HBsAG but HB core antibody (HBcAb) positive (regardless of HBsAb status), a HB deoxyribonucleic acid (DNA) test will be performed; if positive the subject will be excluded * Active hepatitis C infection (HC) defined as a positive test for hepatitis C antibody (HCAb), in which case the investigator should reflexively perform a HC Recombinant Immunoblot assay (RIBA) on the same sample to confirm the result * Known lymphoma involvement of the central nervous system (CNS)