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Lattice structures composed of periodic solid frames and pores can be utilized in energy absorption applications due to their high specific strength and large deformation. However, these structures typically suffer from post-yield softenings originating from the limited plasticity of available material choices. This study aims to resolve such an issue by fabricating lattice structures made of ductile pure copper (Cu). For the first time, Cu lattice structures are fabricated through laser-powder bed fusion (L-PBF) with green laser (λ = 515 nm). Structural and microstructural analysis confirm that the lattice structures consist of well-defined unit cells and show dense microstructure. The deformation behavior is investigated under a wide range of strain rates from ~0.001 /s to ~1000 /s. The stress-strain curves exhibit a smooth and continuous deformation without any post-yield softening, which can be attributed to the intrinsic mechanical properties of Cu. Correlated with post-mortem microscopy examination, the rate-dependent deformation behavior of pure Cu lattice structures is investigated and rationalized. The current work suggests that the complex Cu architectures can be fabricated by L-PBF with green laser and the lattice structures made of ductile metal are suitable for dynamic loading applications.