Herein, we investigate the low-velocity impact behavior of polypropylene random copolymer (PPR)/multi-wall carbon nanotube (MWCNT) and high-density polyethylene (HDPE)/MWCNT plate-lattices processed via fused filament fabrication additive manufacturing, utilizing in-house nanoengineered filament feedstocks. We examine the dynamic crushing and energy absorption characteristics of three typical elementary plate-lattices, namely, simple cubic (SC), body-centered cubic (BCC) and face-centered cubic (FCC) as well as three hybrid plate-lattices (SC-BCC, SC-FCC and SC-BCC-FCC) comprising different weight fractions of MWCNTs at different impact energy levels. The results reveal that the SC-BCC-FCC nanocomposite plate-lattice offers the most favorable impact response as each constituent plate in the lattice contributes to the load carrying capacity for all direction vectors included in the plane of the plate. Furthermore, the results show that impregnating MWCNTs into the PPR and HDPE plate-lattices significantly influences their impact energy attenuation characteristics. Compared with the respective unreinforced plate-lattices, PPR/6 wt% MWCNT SC-BCC-FCC plate-lattices evince higher energy absorption (70%) than HDPE/6 wt% MWCNT SC-BCC-FCC plate-lattices (47%) due to uniform MWCNT dispersion and effective interfacial interaction of MWCNTs in PPR matrix. Our hybrid 3D plate-lattices exhibit a specific energy absorption (SEA) capacity as high as 19.9 J/g, demonstrating their superior impact performance over aluminum and other conventional lattices.