This is an open label, phase 1 dose escalation trial of BTM-3566 in relapsed/refractory mature b cell lymphomas. Dose escalation will utilize traditional 3+3 methodology to determine the maximum tolerated dose of BTM-3566. Treatment will be given as two-week cycles, with BTM-3566 taken daily during the first week of the cycle, and the second week 'off therapy'. DLT window will be the first two cycles of therapy (days 1 to 28). All enrolled patients will undergo a baseline FDG-PET/CT scan within 3 weeks prior to starting therapy. FDG-PET/CT will be repeated at the start of Cycles 3 and 5 or more frequently as clinically indicated. Beginning at Cycle 5, imaging will be repeated every 3 months (or as clinically indicated) for up to 12 months, and every 6 months thereafter, until disease progression or start of subsequent anti-cancer therapy.