The dependence of the fracture toughness of two dimensional elasto-plastic lattices upon relative density and ductility of cell wall material is obtained for four topologies: the triangular lattice, kagome lattice, diamond lattice, and the hexagonal lattice. Crack tip fields are explored, including the plastic zone size and crack opening displacement. The cell walls are treated as beams, with a material response given by the Ramberg-Osgood law. There is choice in the criterion for crack advance, and two extremes are considered: (i) the maximum local tensile strain anywhere in the lattice attains the failure strain, or (ii) the average tensile strain across the cell wall attains the failure strain (which can be identified with the necking strain). The dependence of macroscopic fracture toughness upon failure strain, strain hardening exponent and relative density are obtained for each lattice, and scaling laws are derived. The role of imperfections in degrading the fracture toughness is assessed by random movement of the nodes. The paper provides a strategy for obtaining lattices of high toughness at low density, thereby filling gaps in material property space.