Porous carbons have drawn significant scientific interest, mainly due to carbon's chemical stability, affordability, and exceptional surface area. These materials find applications in diverse areas such as energy storage devices, water contaminant adsorption, and gas separation. Emulsion templating followed by pyrolysis is a promising method to fabricate hierarchically porous carbon materials with interconnected pores at various scales and high surface areas. Combining this technique with additive manufacturing, in particular vat photopolymerization, offers opportunities for creating intricate, inherently porous materials with hierarchical porosity, including carbon lattice structures. Using high internal phase emulsions (HIPEs) as resin for vat photopolymerization allows for the fabrication of templates with multiscale (10 mu m and 100 mu m) porosity- which is challenging for 3D printing. This study investigated the use of inherently porous 3D-printed polymerized High Internal Phase Emulsion (polyHIPE) lattice structures to fabricate hierarchically porous carbonized High Internal Phase Emulsion (carboHIPE) lattices. Surfactant-stabilized water-in-oil emulsions, based on 2-ethylhexyl-acrylate and isobornylacrylate as a 3D printing resin, were used to produce polyHIPE lattices with three distinct porosities (80 %, 85 %, and 87.5 %). The inherently porous lattice-shaped polyHIPEs were pyrolyzed at various temperatures (500 degrees C, 600 degrees C, 700 degrees C, and 800 degrees C) to fabricate carboHIPE lattices. Overall, this study introduced a novel method for fabricating hierarchically porous carboHIPE lattice structures using a combination of emulsion templating and additive manufacturing, followed by pyrolysis. This approach highlighted the challenge of directly achieving micro-sizes in the final shape but also demonstrated that the shrinkage during pyrolysis could be beneficial for creating hierarchically porous microlattice carbon structures.