Copanlisib and Venetoclax for the Treatment of Relapsed or Refractory Mantle Cell Lymphoma

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative * Assent, when appropriate, will be obtained per institutional guidelines * Agreement to allow the use of archival tissue from diagnostic tumor biopsies * If unavailable, exceptions may be granted with study principal investigator (PI) approval * Age: \>= 18 years * Eastern Cooperative Oncology Group (ECOG) =\< 2 * Life expectancy \>= 3 months (per physician assessment) * Ability to take oral medication * Pathologically confirmed MCL, with documentation of monoclonal B cells showing one of the following: * Overexpression of cyclin D1 in association with other relevant markers (e.g., CD19, CD20, PAX5, CD5), OR * Chromosomal translocation t(11;14)(q13; q32), as assessed by cytogenetics, fluorescent in situ hybridization (FISH), or polymerase chain reaction (PCR) * Documented failure to achieve at least partial response (PR) with, or documented disease progression after the most recent treatment regimen * At least 1 prior treatment regimen for MCL which either included chemo-immunotherapy or a targeted agent (i.e., ibrutinib) administered for at least 2 cycles * Have radiologically measurable lymphadenopathy or extranodal lesion, (defined as \>= 1 lesion that measures \>= 2.0 cm in the longest diameter), or splenomegaly, or bone marrow involvement with or without malignant lymphocytosis * Absolute neutrophil count (ANC) \>= 1,000/mm\^3 without bone marrow inv…