The mechanical behaviors of lattice structures can be tuned by arranging or adjusting their geometric parameters. Once fabricated, the lattice’s mechanical behavior is generally fixed and cannot adapt to environmental change. In this paper, we developed a shape reconfigurable, highly stretchable lattice structure with tunable Poisson’s ratio. The lattice is built based on a hexagonal honeycomb structure. By replacing the straight beam with curled microstructure, the stretchability of the lattice is significantly improved. The Poisson’s ratio is adjusted using a geometric angle. The lattice is 3D printed using a shape memory polymer. Using its shape memory effect, the lattice demonstrates tunable shape reconfigurability as the ambient temperature changes. To capture its high stretchability, tunable Poisson’s ratio and shape reconfigurability, a phase evolution model for lattice structure is used. In the theoretical model, the effects of temperature on the material’s nonlinearity and geometric nonlinearity due to the lattice structure are assumed to be decoupled. The theoretical shape change agrees well with the Finite element results, while the theoretical model significantly reduces the computational cost. Numerical results show that the geometrical parameters and the ambient temperature can be manipulated to transform the lattice into target shapes with varying Poisson’s ratios. This work provides a design method for the 3D printed lattice structures and has potential applications in flexible electronics, soft robotics, and biomedicine.