Metallic lattice structures are well known for having high specific elastic moduli and strength. However, very little is understood about their resistance to fracture. In this work Ti–6Al–4V lattice structures are additively manufactured by selective laser melting and their fracture toughness characteristics are investigated. Resistance to fracture was determined under Mode-I loading at static rates using an extended compact tension (EC(T)) specimen, modified to contain lattice cells. The lattices consist of octet cells with a 3.5 mm edge length and relative densities ranging from 25% to 56%. Toughness is shown to increase by a power law with relative density and this trend was also obtained with finite element models. A new functional grading optimisation methodology is also presented for increasing fracture toughness. The size optimisation results in a functionally graded lattice whereby lattice truss diameters become the design variables. After size optimisation, initiation fracture toughness increases by up to 37%.