Recent developments in Civil Engineering proposed the application of structural topology optimisation to buildings and civil engineering structures. Aerospace and automotive engineers routinely employ topology optimisation and have reported significant structural performance gains as a result. Recently designers of buildings and structures have also started investigating the use of topology optimisation, for the design of efficient and aesthetically pleasing developments. This paper exploits computational structural topology optimisation (STO) to deliver a novel exoskeleton for lattice self-supporting telecommunication towers. Topology optimisation (TO) employs intelligent mathematical algorithms to generate 2D layouts or fine 3D models representing structural skeletons, suitable to prescribed forms, with intriguing architectural features and improved weight-to-stiffness ratio. The present study investigates the potentials on delivering a lattice novel tower morphology through both 2D. In particular, a new topology representing a single face of a lattice self-supported tower composed of ‘high-waisted’ bracing type was created using 2D STO with a sequential rationale. Conclusions are drawn with respect to the optimisation analyses (OA) major observations and the potential advantages of STO to the design of lattice telecommunication towers or other similar exoskeleton structures