This study evaluates topologically optimized lattice structures for high strain rate loading, crucial for impact resistance. Using the BESO (Bidirectional Evolution Structural Optimisation) topology optimisation algorithm, CompIED and ShRIED topologies are developed for enhanced energy absorption and impact resistance. Micromechanical simulations reveal CompIED surpasses theoretical elasticity limits for isotropic cellular materials, while the hybrid design ShRComp achieves theoretical maximum across all relative densities. Compared to TPMS, truss, and plate lattices, the proposed structures exhibit higher uniaxial modulus. Manufactured via fused deposition modeling with ABS thermoplastic, their energy absorption capabilities are assessed through compression tests and impact simulations. The ShRComp lattice demonstrates superior energy absorption under compression compared to CompIED. Impact analyses of CompIED and ShRComp sandwich structures at varying velocities show exceptional resistance to perforation and higher impact absorption efficiency, outperforming other classes of sandwich structures at similar densities. These findings position these new and novel topologies as promising candidates for impact absorption applications.