Lisocabtagene Maraleucel, Nivolumab and Ibrutinib for the Treatment of Richter's Transformation

Inclusion Criteria:

* Documented informed consent of the participant
* Agreement for confirmatory pre-treatment tumor biopsy

  * If a patient does not have an easily accessible lymph node to biopsy without excessive risk in the opinion of the investigator, archival biopsy material reviewed by a hematopathologist at the enrolling site for study eligibility and baseline correlatives may be acceptable with approval from the Study principal investigator (PI)
* Age: \>= 18 years
* Eastern cooperative oncology group (ECOG) \<= 2
* Histologically confirmed Richter's Transformation (RT)
* Relapsed / refractory following \>=2 prior lines of systemic therapy; OR refractory to first-line chemoimmunotherapy; OR relapsed within 12 months of first line chemoimmunotherapy; OR relapsed after first line of chemoimmunotherapy and not eligible for hematopoietic stem cell transplantation due to comorbidities or age
* Eligible to receive liso-cel and ibrutinib per package inserts
* Fully recovered from the acute toxic effects (except alopecia) to \<= Grade 1 to prior anti-cancer therapy
* Absolute neutrophil count (ANC) \>= 750/mm\^3 unless there is bone marrow involvement
* Platelets \>= 75,000/mm\^3 unless there is bone marrow involvement
* Total bilirubin =\< 1.5 X ULN (unless has Gilbert's disease)
* Aspartate aminotransferase (AST) =\< 2.5 x ULN
* Alanine aminotransferase (ALT) =\< 2.5 x ULN
* Creatinine clearance of \>= 30 mL/min per 24 hour urine test or the Cockcroft-Gault formula
* International Normalized Ratio (INR) OR Prothrombin (PT) =\< 1.5 x ULN
* Activated Partial Thromboplastin Time (aPTT) =\< 1.5 x ULN
* Left ventricular ejection fraction (LVEF) \>= 40%

  * Note: To be performed within 28 days prior to Day 1 of protocol therapy.
* Seronegative for HCV\*, active HBV (Surface Antigen Negative), and syphilis (RPR)

  * If positive, Hepatitis C RNA quantitation must be performed OR
  * If seropositive for HCV or HBV, nucleic acid quantitation must be performed. Viral load must be undetectable
* Meets other institutional and federal requirements for infectious disease titer requirements

  * Note: Infectious disease testing to be performed within 28 days prior to Day 1 of protocol therapy
* Women of childbearing potential (WOCBP): negative urine or serum pregnancy test

  * If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required
* Agreement by females and males of childbearing potential\* to use an effective method of birth control or abstain from heterosexual activity for the course of the study through at least 5 months after the last dose of protocol therapy

  * Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only)

Exclusion Criteria:

* Subjects who previously received PD1 or PD-L1 inhibitor therapy
* Autologous stem cell transplant within 3 months prior to Day 1 of protocol therapy
* Allogeneic stem cell transplant within 3 months prior to Day 1 of protocol therapy and no active graft versus host disease (GVHD) or need for immunosuppressants
* Chemotherapy, radiation therapy, immunotherapy within 14 days prior to Day 1 of protocol therapy
* Strong CYP3A inducers within 14 days prior to Day 1 of protocol therapy
* Warfarin within 5 days prior to Day 1 of protocol therapy
* Current requirement for oxygen supplementation
* Concurrent use of systemic steroids or chronic use of immunosuppressant medications. Recent or current use of inhaled steroids is not exclusionary. Physiologic replacement of steroids (prednisone =\< 7.5 mg /day or equivalent) is allowed throughout the study. Use of "bridging" steroids, to control disease, after leukapheresis and until 3 days prior to CAR T cell infusion, is allowed
* Subjects with lymphoma only involving the central nervous system
* Class III/IV cardiovascular disability according to the New York Heart Association (NYHA) Classification
* Subjects with clinically significant arrhythmia or arrhythmias not stable on medical management within two weeks of screening
* Subjects with a known history or prior diagnosis of optic neuritis or other immunologic or inflammatory disease affecting the central nervous system, including seizure disorder
* Subjects with a history of allergic reactions attributed to compounds of similar chemical or biologic composition to study agent
* Known bleeding disorders (e.g., von Willebrand's disease) or hemophilia
* History of stroke or intracranial hemorrhage within 6 months prior to screening
* History of other malignancies, except for malignancy surgically resected (or treated with other modalities) with curative intent, basal cell carcinoma of the skin or localized squamous cell carcinoma of the skin; non-muscle invasive bladder cancer; malignancy treated with curative intent with no known active disease present for \>= 3 years
* Clinically significant uncontrolled illness
* Active infection requiring antibiotics
* Known history of immunodeficiency virus (HIV)
* Females only: Pregnant or breastfeeding
* Subjects with an active, known or suspected autoimmune disease. Subjects with type I diabetes mellitus, hypothyroidism only requiring hormone replacement, skin disorders (such as vitiligo, psoriasis) not requiring systemic treatment, well controlled asthma and/or mild allergic rhinitis (seasonal allergies) are eligible
* Any other condition that would, in the Investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures
* Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)