Testing the Addition of an Immunotherapy Agent, Atezolizumab, When Given With the Usual Chemo-Immunotherapy Drug Combination (Rituximab Plus Gemcitabine and Oxaliplatin) for Relapsed/Refractory (That Has Come Back or Not Responded to Treatment) Transformed Diffuse Large B-Cell Lymphoma

• Patients must have histologically confirmed transformed diffuse large B-cell lymphoma (DLBCL), including histologic transformation from any indolent lymphoma (e.g. follicular or marginal zone lymphoma) or Richter transformation of chronic lymphocytic leukemia/small lymphocytic lymphoma (CLL/SLL)
• Patients must have measurable disease by CT or PET scan, with one or more sites of disease >= 1.5 cm in longest dimension
• Relapsed or refractory disease after at least 1 prior regimen, defined using the 2014 Lugano classification
• Age >= 18 years. Because no dosing or adverse event data are currently available on the use of atezolizumab in patients \<18 years of age, children are excluded from this study, but will be eligible for future pediatric trials
• Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky >= 60%)
• Life expectancy of greater than 3 months
• Leukocytes >= 2,500/mcL, unless documented bone marrow involvement by lymphoma
• Absolute neutrophil count >= 1,000/mcL, unless documented bone marrow involvement by lymphoma
• Platelets >= 75,000/mcL, unless documented bone marrow involvement by lymphoma
• Hemoglobin >= 8 g/dL, unless documented bone marrow involvement by lymphoma
• Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) (however, patients with known Gilbert disease who have serum bilirubin level =\< 3 x ULN may be enrolled)
• Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =\< 3 x ULN (AST and/or ALT =\< 5 x ULN for patients with liver involvement)
• Alkaline phosphatase =\< 2.5 x ULN (=\< 5 x ULN for patients with documented liver involvement or bone metastases)
• Creatinine clearance >= 30 mL/min/1.73 m\^2 by Cockcroft-Gault
• International normalized ratio (INR) and partial thromboplastin time (aPTT) =\< 1.5 x ULN (this applies only to patients who do not receive therapeutic anticoagulation; patients receiving therapeutic anticoagulation, such as low-molecular-weight heparin or warfarin, should be on a stable dose)
• Administration of atezolizumab may have an adverse effect on pregnancy and poses a risk to the human fetus, including embryo-lethality; women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 5 months (150 days) after the last dose of study agent; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately
• Ability to understand and the willingness to sign a written informed consent document

• Patients positive for human immunodeficiency virus (HIV) are allowed on 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 tests

Exclusion Criteria:

• Patients with prior allogeneic bone marrow transplantation or prior solid organ transplantation
• Patients who have previously received gemcitabine plus oxaliplatin therapy

• Patients who have had chemotherapy or radiotherapy within 2 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events (other than alopecia) due to agents administered more than 2 weeks earlier; however, the following therapies are allowed:

  • Hormone-replacement therapy or oral contraceptives
  • Herbal therapy > 1 week prior to cycle 1, day 1 (herbal therapy intended as anticancer therapy must be discontinued at least 1 week prior to cycle 1, day 1)

• Prior treatment with anti-PD-1, or anti-PD-L1 therapeutic antibody or pathway-targeting agents

  • Patients who have received prior treatment with anti-CTLA-4 may be enrolled, provided the following requirements are met:

    • Minimum of 12 weeks from the first dose of anti-CTLA-4 and > 6 weeks from the last dose
    • No history of severe immune-related adverse effects from anti-CTLA-4 (National Cancer Institute [NCI] Common Terminology Criteria for Adverse Events [CTCAE] version 5.0)
• Treatment with any other investigational agent within 3 weeks prior to cycle 1, day 1
• Treatment with systemic immunostimulatory agents (including, but not limited to, interferon [IFN]-alpha or interleukin [IL]-2) within 6 weeks prior to cycle 1, day 1

• Treatment with systemic immunosuppressive medications (including, but not limited to, prednisone, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor [anti-TNF] agents) within 2 weeks prior to cycle 1, day 1

  • Patients who have received acute, low dose, systemic immunosuppressant medications (e.g., a one-time dose of dexamethasone for nausea) may be enrolled
  • The use of inhaled corticosteroids and mineralocorticoids (e.g., fludrocortisone) for patients with orthostatic hypotension or adrenocortical insufficiency is allowed
• Patients taking bisphosphonate therapy for symptomatic hypercalcemia; use of bisphosphonate therapy for other reasons (e.g., bone metastasis or osteoporosis) is allowed
• Patients requiring treatment with a RANKL inhibitor (e.g. denosumab) who cannot discontinue it before treatment with atezolizumab
• Patients with known active central nervous system (CNS) involvement by lymphoma, including leptomeningeal involvement
• Known hypersensitivity to Chinese hamster ovary cell products or other recombinant human antibodies
• History of severe allergic, anaphylactic, or other hypersensitivity reactions to chimeric or humanized antibodies or fusion proteins
• History of allergic reactions attributed to compounds of similar chemical or biologic composition to other agents used in study

• Known clinically significant liver disease, including active viral, alcoholic, or other hepatitis; cirrhosis; fatty liver; and inherited liver disease

  • Patients with past or resolved hepatitis B infection (defined as having a negative hepatitis B surface antigen [HBsAg] test and a positive anti-HBc [antibody to hepatitis B core antigen] antibody test) are eligible
  • Patients positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction (PCR) is negative for HCV ribonucleic acid (RNA)

• History or risk of autoimmune disease, including, but not limited to, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, vascular thrombosis associated with antiphospholipid syndrome, Wegener's granulomatosis, Sjogren's syndrome, Bell's palsy, Guillain-Barre syndrome, multiple sclerosis, autoimmune thyroid disease, vasculitis, or glomerulonephritis

  • Patients with a history of autoimmune hypothyroidism on a stable dose of thyroid replacement hormone may be eligible
  • Patients with controlled type 1 diabetes mellitus on a stable insulin regimen may be eligible

  • Patients with eczema, psoriasis, lichen simplex chronicus of vitiligo with dermatologic manifestations only (e.g., patients with psoriatic arthritis would be excluded) are permitted provided that they meet the following conditions:

    • Patients with psoriasis must have a baseline ophthalmologic exam to rule out ocular manifestations
    • Rash must cover less than 10% of body surface area (BSA)
    • Disease is well controlled at baseline and only requiring low potency topical steroids (e.g., hydrocortisone 2.5%, hydrocortisone butyrate 0.1%, fluocinolone 0.01%, desonide 0.05%, alclometasone dipropionate 0.05%)
    • No acute exacerbations of underlying condition within the last 12 months (not requiring psoralen plus ultraviolet A radiation [PUVA], methotrexate, retinoids, biologic agents, oral calcineurin inhibitors; high potency or oral steroids)
• History of idiopathic pulmonary fibrosis, pneumonitis (including drug induced), organizing pneumonia (i.e., bronchiolitis obliterans, cryptogenic organizing pneumonia, etc.), or evidence of active pneumonitis on screening chest computed tomography (CT) scan; history of radiation pneumonitis in the radiation field (fibrosis) is permitted
• Patients with active tuberculosis (TB) are excluded
• Severe infections within 4 weeks prior to cycle 1, day 1, including, but not limited to, hospitalization for complications of infection, bacteremia, or severe pneumonia
• Signs or symptoms of infection within 2 weeks prior to cycle 1, day 1
• Received oral or intravenous (IV) antibiotics within 2 weeks prior to cycle 1, day 1; patients receiving prophylactic antibiotics (e.g., for prevention of a urinary tract infection or chronic obstructive pulmonary disease) are eligible
• Major surgical procedure within 28 days prior to cycle 1, day 1 or anticipation of need for a major surgical procedure during the course of the study

• Administration of a live, attenuated vaccine within 4 weeks before cycle 1, day 1 or anticipation that such a live, attenuated vaccine will be required during the study and up to 5 months after the last dose of atezolizumab

  • Influenza vaccination should be given during influenza season only (approximately October to March); patients must not receive live, attenuated influenza vaccine within 4 weeks prior to cycle 1, day 1 or at any time during the study
• Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
• Pregnant women are excluded from this study because atezolizumab, gemcitabine, and oxaliplatin are agents with the potential for teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with atezolizumab, gemcitabine, and oxaliplatin, breastfeeding should be discontinued if the mother is treated with atezolizumab, gemcitabine, and oxaliplatin; these potential risks may also apply to other agents used in this study