Designing structures that effectively dissipate energy across a broad range of mechanical loading rates, including those from compression, shock, and vibration, poses a significant engineering challenge. In this study, liquid‐crystal elastomers (LCEs), which possess anisotropic properties due to the alignment of their polymer backbone, are explored. As a result, LCEs exhibit a soft elastic response under mechanical loading, making them ideal for energy dissipation. Advances in additive manufacturing (AM) enable simple fabrication of foamlike dissipative structures with complex lattice geometries. Herein, direct ink write 3D printing, an extrusion AM method, is used to fabricate aligned, monodomain LCE lattice structures for broad strain‐rate mechanical damping. In this work, it is shown that these structures can dissipate strain energy in quasi‐static environments, comparable to traditional elastomeric lattices, and provide improved damping under high strain‐rate drop testing due to LCE soft elasticity. Additionally, under dynamic mechanical vibration, monodomain LCE lattices enhance damping at structural natural frequencies and provide high‐frequency attenuation. In these findings, a promising method is presented for fabricating mechanical damping devices that effectively dissipate energy across a broad range of loading rates.