This study investigates the quasi-static and dynamic compression performance of a newly designed stacked pyramidal lattice (SPL) structure composed of struts that resemble I-beams. These novel lattice structures are 3D-printed considering three different stacking sequences, and their stiffness, strength, and energy absorption properties are experimentally assessed through low-velocity impact (1.54 m/s) and quasi-static compression tests. Additionally, dynamic finite element (FE) simulations are carried out to delve deeper into the collapse mechanisms and failure processes. The findings indicate that the SPLs with I-beam struts outperform conventional SPLs with square struts of same mass showcasing superior rigidity, durability, and energy absorption. Specifically, we report enhancements in strength and energy absorption of 26% and 109% under quasi-static compression and 34% and 74% under low-velocity impact, respectively. The latter enhancements are attributed to the improved transverse bending stiffness of the I-shaped cross-section, resulting in lateral (sideward) buckling of the lattice struts. Both experimental and numerical findings demonstrate that altering the stacking sequence of the SPL can lead to significant improvements in the dynamic compression performance, with enhancements of up to 84% in collapse strength.