Lattice structures with lattice parameters in the mm range are routinely fabricated by additive manufacturing. Combining light weight and mechanical strength, these structures have plenty of potential applications. When composed of conducting elements, a 3D lattice has interesting electrical and electromagnetic properties. In this work, the electrokinetic properties of a conducting lattice are described by mixing the theory of resistor networks and continuous-medium electrodynamics. Due to the length scale provided by the lattice parameter, the effective continuous medium that mimics the electrokinetic response of a resistor lattice is characterized by a non-local Ohm’s law.