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Porous graphene and graphite are increasingly utilized in electrochemical energy storage and solar-thermal applications due to their unique structural and thermal properties. In this study, we conduct a comprehensive analysis of the lattice thermal transport and spectral phonon characteristics of holey graphite and multilayer graphene. Our results reveal that phonon modes propagating obliquely with respect to the graphene basal planes are the primary contributors to cross-plane thermal transport. These modes exhibit a predominantly ballistic nature, resulting in an almost linear increase in cross-plane thermal conductivity with the number of layers. The presence of nanoholes in graphene induces a broadband suppression of cross-plane phonon transport, whereas lithium-ion intercalation shows potential to enhance it. These findings provide critical insights into the mechanisms governing cross-plane heat conduction in key graphene-based structures, offering valuable guidance for thermal management and engineering of van der Waals materials.