Lattice structures fabricated by additive manufacturing (AM) possess unique properties, namely high compressive strength, low density, large surface area, etc. Secondary processing for fastening, implantation, and installation necessitates machining of AM lattice structures. Electrical discharge machining (EDM) process, owing to the non-contact material removal mechanism, allows deformation-free machining of such lattice structures, which are otherwise deformed and sometimes damaged while machining using contact-based deformation and machining processes. In the current work, EDM hole drilling operation is conducted on laser powder bed fusion (LPBF) based IN718 lattice structure. The challenge in drilling through holes using EDM drilling has been encountered. The uncertainty in the machined hole dimensions with respect to varying tool electrode diameter has been identified due to periodically open pores in the parent lattice structure. EDM drilling operation has been conducted using a tungsten tool of 900 µm diameter with varying currents (4-10 A), pulse-on times (50-150 µs) and duty-ratios (56-80 %) as input process variables. The initial results suggest a noticeable variation in machining rate, machined feature size and shape and tool wear, primarily due to the tool positioning with respect to the lattice geometry and nodal locations, i.e., fraction open pore or solid material. Efforts are being made to determine the strategies for generating near-circular features by designing and positioning of the tool with respect to the pore size and solid walls.