Structural glass beams and fins are used as primary load-bearing members and bracing systems for roof or facade panels. The intrinsic features and vulnerability of the constituent materials, however, is known to require dedicated calculation methods for their safe structural design. Among other issues, glass fins are often characterized by high slenderness, and can be thus susceptible to premature Lateral Torsional Buckling (LTB) phenomena. While literature studies are available for the LTB analysis of laterally unrestrained (LU) glass elements, practical calculation methods and design recommendations are still weak for members that take advantage of discrete lateral restraints (LRs). This study focuses on the LTB assessment of LR glass beams with LR mechanical connectors, where relatively stiff point fixings are expected to locally restraint the brittle members, via glass holes.