This work introduces an innovative framework for the topological optimization of periodic lattice metamaterials, specifically designed to maximize its macroscopic electromechanical response. Through appropriate geometrical design, periodic lattice metamaterials can deliver a macroscopic apparent piezoelectric response using non-piezoelectric base materials by upscaling the flexoelectric local response of small scale lattice features. Flexoelectric metamaterials thus provide a promising potential alternative to piezoelectric materials for electromechanical applications. Flexoelectricity is the two-way coupling between strain gradient and polarization, and conversely the coupling between polarization gradient and strain. It is modeled mathematically as a coupled system of fourth-order PDEs. The flexoelectric response of lattice metamaterials is highly dependent on small geometrical features, which poses challenges on their topological optimization . A distinctive feature of the present framework is its ability to represent complex geometries with smooth contours and control minimum thickness, integrating bit-array representations and the levelset method.\\ The second key aspect of this framework is the successful resolution of the continuity problem in lattice patterns, resulting in a more efficient and effective optimization process. By ensuring connectivity between unit cells in the lattice, it avoids discarding patterns due to disconnection, enhancing the viability of the optimized structures. The resulting desings surpass conventional piezoelectric materials in certain modes of electromechanical transduction.