Additively manufactured lattice structures enable the realisation of light-weight, multi-functional, structures. For example, lattices can be used for high stiffness and buckling resistance in sandwich structures or as support material for additive manufacturing. Topology optimisation and additive manufacturing are two technologies that allow the design, optimisation and manufacture of complex lattice designs. In this work, a new lattice optimisation methodology is presented that tailors the size, shape and orientation of individual lattice trusses in three-dimensional space by using principal strain fields obtained from topology optimisation. This new method of generating functionally graded lattices is shown both numerically and experimentally to be capable of generating lattice structures with greatly improved stiffness and strength when compared to lattice structures with a uniform lattice infill. Upper and lower relative density thresholds and minimum truss member sizes are included in the optimisation workflow to ensure that the optimised lattice designs are compatible with additive manufacturing process constraints. The functional grading method is also shown to be capable of generating conformal lattice structures in three dimensions, even for complex loading conditions and arbitrary volume boundaries.