Inclusion Criteria:  Male or female participant aged 18 years or older Pathologic diagnosis of relapsed (disease that has recurred following a response) or refractory (disease that failed to respond to prior therapy) B-cell non-Hodgkin Lymphoma (B-NHL) (2016 World Health Organization classification) who have failed, or been intolerant to any approved therapy and had received at least two systemic treatment regimens Participants who have received previous cluster of differentiation 19 (CD19)-directed therapy must have a biopsy that shows CD19 expression after completion of the CD19-directed therapy Need of systemic treatment for any of the listed indications as assessed by the investigator, including indolent B-NHLs (e.g. follicular lymphoma [FL] and marginal zone lymphoma [MZL]) Measurable disease as defined by the 2014 Lugano Classification Availability of formalin-fixed paraffin-embedded tumor tissue block Eastern Cooperative Oncology Group performance status 0 to 2 Adequate organ function Women of childbearing potential (WOCBP) must agree to use a highly effective method of contraception from the time of giving informed consent (for the arm that includes lenalidomide, from at least 4 weeks before starting lenalidomide) until at least 9 months after the last dose of study drug. Men with female partners who are of childbearing potential must agree to use a highly effective method of contraception from the time of giving informed consent until at least 6 months after the last dose of study drug  Exclusion Criteria:  Known history of hypersensitivity resulting in treatment discontinuation to or positive serum human anti-drug antibody (ADA) to a CD19 antibody Known history of hypersensitivity to gemcitabine, lenalidomide, polatuzumab vedotin, or umbralisib leading to treatment discontinuation (applied to relevant arm and/or cohort of the specific drug administered) Previous therapy with loncastuximab tesirine Previous treatment of gemcitabine, lenalidomide, polatuzumab vedotin or umbralisib (applied to relevant arm and/or cohort of the specific drug administered) Allogenic or autologous stem cell transplant within 60 days prior to start of study drug Cycle 1, Day 1 (C1D1) (cycle is 21 days) Human immunodeficiency virus (HIV) seropositive Serologic evidence of chronic hepatitis B virus (HBV) infection and unable or unwilling to receive standard prophylactic antiviral therapy or with detectable HBV viral load Serologic evidence of hepatitis C virus (HCV) infection without completion of curative treatment or with detectable HCV viral load For the arm that includes umbralisib, confirmed cytomegalovirus (CMV) infection (participants who are CMV immunoglobulin G [IgG] or immunoglobulin M [IgM] positive but CMV deoxyribonucleic acid [DNA] negative by polymerase chain reaction [PCR] are eligible) For the arm that includes umbralisib, history of or ongoing inflammatory bowel disease History of Stevens-Johnson syndrome or toxic epidermal necrolysis Lymphoma with active central nervous system (CNS) involvement at the time of screening, including leptomeningeal disease Clinically significant third space fluid accumulation (i.e., ascites requiring drainage or pleural effusion that is either requiring drainage or associated with shortness of breath) Breastfeeding or pregnant Significant medical comorbidities Major surgery, radiotherapy, chemotherapy, or other anti-neoplastic therapy, within 14 days prior to start of study drugs (C1D1; cycle is 21 days), except shorter if approved by the Sponsor