This paper tests the low-energy (120 J) drop-weight impact behavior of composite sandwich panels composed of additively manufactured Stainless Steel 316L (SS316L) sheet-based TPMS-lattice cores and fiber-reinforced composite skins. The effect of TPMS-lattice core topologies (Gyroid, Diamond, Primitive, and I-Wrapped Package), relative densities (8, 10%, 15% and 20%), and cell sizes (5 mm and 10 mm) on the drop-weight impact behavior and multi-hit capabilities of the composite sandwich panels is studied. Micro-computed tomography (CT) characterization is conducted to assess the internal damage and deformation pattern of the core within the impact zone. The micro-CT scans revealed that higher densities and cell size in the lattice core improve resistance to damage with enhanced composite skin protection during impact loading. The nature of the Gyroid architecture facilitated load distribution and enhanced the resistance of the composite sandwich panel to impact loading. However, during the multi-hit scenarios, the combined high uniaxial and shear properties of the Diamond architecture and the effect of lattice densification near the projectile contributed to providing superior impact resistance and energy absorption. Thus, the study has facilitated decision-making on selecting the appropriate sheet-based TPMS-lattice core topological features for designing composite sandwich panels that meet specific structural engineering needs.