Nematic liquid crystal elastomers (LCEs) are a unique class of network polymers with the potential for enhanced mechanical energy absorption and dissipation capacity over conventional network polymers because they exhibit both conventional viscoelastic behavior and soft-elastic behavior (nematic director changes under shear loading). This additional inelastic mechanism makes them appealing as candidate damping materials in a variety of applications from vibration to impact. The lattice structures made from the LCEs provide further mechanical energy absorption and dissipation capacity associated with packing out the porosity under compressive loading.Understanding the extent of mechanical energy absorption, which is the work per unit mass (or volume) absorbed during loading, versus dissipation, which is the work per unit mass (or volume) dissipated during a loading cycle, requires measurement of both loading and unloading response. In this study, a bench-top linear actuator was employed to characterize the loading-unloading compressive response of polydomain and monodomain LCE polymers and polydomain LCE lattice structures with two different porosities (nominally, 62% and 85%) at both low and intermediate strain rates at room temperature. As a reference material, a bisphenol-A (BPA) polymer with a similar glass transition temperature (9 °C) as the nematic LCE (4 °C) was also characterized at the same conditions for comparing to the LCE polymers. Based on the loading-unloading stress-strain curves, the energy absorption and dissipation for each material at different strain rates (0.001, 0.1, 1, 10 and 90 s-1) were calculated with considerations of maximum stress and material mass/density. The strain-rate effect on the mechanical response and energy absorption and dissipation behaviors was determined. The energy dissipation ratio was also calculated from the resultant loading and unloading stress-strain curves. All five materials showed significant but different strain rate effects on energy dissipation ratio. The solid LCE and BPA materials showed greater energy dissipation capabilities at both low (0.001 s−1) and high (above 1 s−1) strain rates, but not at the strain rates in between. The polydomain LCE lattice structure showed superior energy dissipation performance compared with the solid polymers especially at high strain rates.