Lattice materials, a class of architected material, demonstrate a broad range of mechanical behaviors enabled by the design of their internal geometry and selection of their constituent material. At low relative densities (where the ratio between lattice and base material density is less than 0.3), lattices exhibit high specific toughness compared to traditional engineering materials, and their fracture mechanics are well-understood. However, at relative densities above 0.3, classical lattice fracture models become inaccurate as the stress state in each ligament is no longer accurately captured by simple beam models. As a result, lattice fracture behavior remains less explored in this regime despite a predicted increase in toughness. In this talk, I will discuss the transition in fracture behavior of triangular and hexagonal lattices from low to high relative density, first through a new experimental approach for testing 2D architected materials, then using theoretical and computational modeling of elastic-brittle and elastic-plastic lattices. The results demonstrate that stress concentrations located at the lattice nodes play a significant role in determining failure at high densities and depend on the local geometry at the crack tip, including the lattice relative orientation and fillet radius. Furthermore, material plasticity is shown to enhance toughness by softening stress concentrations and dissipating energy near the crack tip, while also revealing certain geometries with fracture toughness that exceeds that of the base material.