Lattice structures are typically made up of a crisscross pattern of beam elements, allowing engineers to distribute material in a more structurally effective way. However, a main challenge in the design of lattice structures is a trade-off between the density and mechanical properties. Current studies have often assumed the cross-sectional area of the beam elements to be uniform for reducing the design complexity. This simplified approach limits the possibility of finding superior designs with optimized weight-to-performance ratios. Here, the optimized shape of the beam elements is investigated using a deep learning approach with high-order Bézier curves to explore the augmented design space. This is then combined with a hybrid neural network and genetic optimization (NN-GO) adaptive method for the generation of superior lattice structures. In our optimized design, the distribution of material is smartly shifted more towards the joint region, the weakest location of lattice structures, to achieve the highest modulus and strength. This design strikes to balance between two modes of deformation: axial and bending. Thus, the optimized design is efficient for load bearing and energy absorption. To validate our simulations, the optimized design is then fabricated by additive manufacturing and its mechanical properties are evaluated through compression testing. A good correlation between experiments and simulations is observed and the optimized design has outperformed benchmark ones in terms of modulus and strength. We show that the extra design flexibility from high-order Bézier curves allows for a smoother transition between the beam elements which reduces the overall stress concentration profile.