This paper investigates the structure-property relations of thin-walled lattices under dynamic longitudinal compression, characterized by their cross-sections and heights. These relations elucidate the interactions of different geometric features of a design on mechanical response, including energy absorption. We proposed a combinatorial, key-based design system to generate different lattice designs and used the finite element method to simulate their response with the Johnson-Cook material model. Using an autoencoder, we encoded the cross-sectional images of the lattices into latent design feature vectors, which were supplied to the neural network model to generate predictions. The trained models can accurately predict lattice energy absorption curves in the key-based design system and can be extended to new designs outside of the system via transfer learning.