Sandwich panel structures are widely used in aerospace, marine, and automotive applications because of their high flexural stiffness, strength-to-weight ratio, good vibration damping, and low through-thickness thermal conductivity. These structures consist of solid face sheets and low-density cellular core structures, which are traditionally based upon honeycomb folded-sheet topologies. The recent advances in additive manufacturing (AM) or 3D printing process allow lattice core configurations to be designed with improved mechanical properties. In this work, the sandwich core is comprised of lattice truss structures (LTS). Two different LTS designs are 3D-printed using acrylonitrile butadiene styrene (ABS) and are tested under low-velocity impact loads. The absorption energy and the failure mechanisms of lattice cells under such loads are investigated. The differences in energy-absorption capabilities are captured by integrating the load–displacement curve found from the impact response. It is observed that selective placement of vertical support struts in the unit-cell results in an increase in the absorption energy of the sandwich panels.