4D printed structures can change their properties and functionalities as a response to a change in the environmental conditions, such as a change in the temperature. A heat stimulus can be used to trigger a transition between two states of a shape memory polymer. Specially designed structures made from these materials can transform into different shapes at different temperatures and can be useful for applications in morphing wings or car panels. Most of these structures, however, are still designed by hand and possess limited load carrying capabilities in at least one of their states. Here, it is shown how complex lightweight structures with multiple stable states can be designed using material modeling and structural optimization methods. By distributing different materials to different parts of the structure, local stiffness gradients are introduced, giving rise to architected global deformations under a single, locally applied load. The shape deformations can be either continuous over the whole structure or discrete only in small regions. The results demonstrate how active materials can be used in a new way to design shape morphing, lightweight lattice structures with different stable states and without sacrificing their structural capabilities.