Pyramidal lattice structures have frequently been employed as the core material in the design of sandwich panels due to their impressive weight-specific strength. However, the struts in pyramidal lattice structures bend when subjected to axial, shear, or bending loads, leading to non-uniform stress distributions, especially at low relative densities. The current work introduces a geometrical tailoring scheme that provides the designer with additional parameters that can be adjusted to tune the cross-sectional properties of the lattice struts with the goal of obtaining more uniform stress distributions across their thickness. Specifically, the conventional square and circular pyramidal lattice struts are reshaped into I-beam-like cross-sections, forming a tailored pyramidal lattice. These geometrically tailored pyramidal lattices are 3D printed via the Digital Light Processing (DLP) technique. The quasi-static compressive responses of the lattices are experimentally evaluated in terms of elastic modulus, collapse strength, and energy absorption capacity. Additionally, the collapse mechanisms of the geometrically tailored structures were assessed via a non-linear finite element analysis which was validated against the experimental evidence. The results substantiate the validity of the geometrical tailoring strategy as the reported energy absorption capacity of the tailored pyramidal lattice structure exhibits a significant enhancement up to 64% and 15% respectively. The latter enhancements were attributed to the lateral buckling of struts, prompting the tailored struts to bend sideways during the collapse phase.