Loncastuximab Tesirine and Mosunetuzumab for the Treatment of Relapsed or Refractory Diffuse Large B-Cell Lymphoma

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative. * Assent, when appropriate, will be obtained per institutional guidelines. * Be willing to provide tissue from a fresh core or excisional biopsy (performed as standard of care) of a tumor lesion prior to starting study therapy or 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. * Histologically confirmed diagnosis of diffuse large B-cell lymphoma or Follicular Lymphoma Grade 3B according to the World Health Organization (WHO) classification, with hematopathology review at the participating institution. Subtypes of DLBCL including transformed indolent lymphomas (TIL) including Richter's Transformation, primary mediastinal large B-cell lymphoma (PMBCL), and high-grade B-cell lymphoma not otherwise specified (HGBCL-NOS) are eligible. * Life expectancy \> 12 months. * Histologically confirmed diagnosis of diffuse large B-cell lymphoma (DLBCL) or follicular lymphoma Grade 3B according to the WHO classification, with hematopathology review at the participating institution. Subtypes of DLBCL including transformed indolent lymphomas (TIL) including Richter's Transformation, primary mediastinal large B-cell lymphoma (PMBCL), and high-grade B-cell lymphoma not otherwise specified (HGBCL-NOS) are eligible. * Relapsed or refra…