Triply periodic minimal surface (TPMS) structures exhibit significant potential in latent heat storage (LHS) applications. In this study, numerical investigations were conducted to study the thermal storage performance of four TPMS lattice types: Primitive, IWP, FRD, and Gyroid lattices, used as metallic skeletons in LHS devices. The volumes of both the TPMS skeletons and the phase change material (PCM) were kept constant, with PCM embedded either inside or outside the lattices. The melting process of PCM, the heat storage energy density, and the power density of the LHS units for different configurations were examined. Additionally, a performance evaluation coefficient was introduced to assess the heat transfer and flow characteristics of heat transfer fluid (HTF) flowing on both sides of the lattices. The results indicated that when using Primitive and FRD lattices, embedding the PCM within the internal space of the lattices resulted in a 20 % and 9.8 % higher energy storage compared to embedding it outside the lattices. The internal space of IWP and Gyroid lattices was more suitable for HTF flow channels, resulting in performance evaluation coefficients (PECs) that improved by 27.7 % and 86.3 %, respectively, when HTF flowed through the internal channels of these lattices. Moreover, the Gyroid lattice exhibited the most balanced overall heat transfer performance due to its minimal flow resistance, whereas the FRD lattice had the lowest flow performance due to its complex structure. Therefore, the Primitive and Gyroid lattices could be considered as new heat transfer structures for LHS devices, while the FRD lattice was more suitable for replacing traditional fin structures in heat sink devices.