Lattice structures offer unique mechanical properties and versatility in engineering applications, yet existing designs often struggle to balance performance and material efficiency. This study introduces the brachistochrone curve as a novel framework for optimizing lattice geometries, enhancing mechanical behavior while minimizing material usage. Using finite element simulations and compressive testing of 3D-printed samples, we analyzed the mechanical response of brachistochrone-based (B-) and standard lattice structures (diamond, IWP, gyroid, and BCC). We investigated the scaling behavior of the volume-to-surface area ratio, incorporated fractal dimension analysis, and compared experimental and numerical results to evaluate the performance of B-lattices versus standard designs (S-). Our findings indicate that brachistochrone-inspired lattices enhance mechanical efficiency, enabling the design of lightweight, high-strength components with sustainable material use. Experimental results suggest that B-gyroid lattices exhibit lower stiffness than S-gyroid lattices under small displacements, highlighting their potential for energy absorption applications.