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The advance of additive manufacturing makes it possible to design spatially varying lattice structures with complex geometric configurations. The homogenized elastic properties of these periodic lattice structures are known to deviate significantly from isotropic behavior where orthotropic material symmetry is often assumed. This paper addresses the need for a robust homogenization method for evaluating anisotropy of periodic lattice structures including an understanding of how the elastic properties transform under rotation. Here, periodic boundary conditions are applied on two-material representative volume element (RVE) finite element models to evaluate the complete homogenized stiffness tensor. A constrained multi-output regression approach is proposed to evaluate the elasticity tensor components under any assumed material symmetry model. This approach is applied to various lattice structures including scaffold and surface-based Triply Periodic Minimal Surface (TPMS). Our approach is used to assess the accuracy of rotation for assumed anisotropic and orthotropic homogenized material models over a range of lattice structures.