Through advanced computational analysis, this work demonstrates that metamaterial structures when made by shape-memory polymers (SMPs) can provide unique intelligent mechanical behavior. For the first time, geometrical effects, pertaining to low and ultra-low densities, on the thermomechanical behavior of SMP-based octet-truss lattice meta-structures are studied in this work. A reliable constitutive thermo-visco-hyperelastic model is applied to analyze the shape-memory behavior of several designed octet-truss lattices with ultra-low and low relative densities, ranging from 0.04 to 0.23. Different compressive strain values are tested to determine the effect of pre-straining. It is concluded that changing the relative density as a consequence of altering the diameter of struts in lattice meta-structures is a crucial factor affecting their shape-memory properties, deformation mechanism, and macro-scale mechanical properties compared to the bulk SMPs. The finite element results demonstrate that the relative density and pre-strain level provide two controlling parameters in programming the SMP-based lattice meta-structures and enhancing their stress recoverability.