Shape-morphing structures are beneficial for applications in aerospace, automotive, and architecture since they allow structures to adapt to changing environmental conditions. Finding structural configurations with intrinsic shape-morphing capabilities is, however, difficult due to the complexity of enabling and controlling target deformations while at the same time maintaining structural integrity. Existing solutions are often unstable, hard to fabricate, or limited to a single target state. Here, we show how lattice structures can be designed that morph from an initial state to one or multiple target states with a single kinematic degrees-of-freedom. Thus, the deformations of a structure can be fully controlled by controlling a single input node for every state. Since the structures are designed at the verge of kinematic determinacy, they become statically and kinematically determinate and hence load-carrying upon fixing the actuation node. As all deformations are described by inextensional mechanism modes, the kinematic and mechanical performance of the structures are decoupled and can be tuned individually. We further show that not only the target shape of a structure can be controlled, but also the kinematic path of a target node between its initial and its final position. The results are verified by fabricating the designs using multi-material 3D printing that enables direct fabrication of complex joints. Our work combines advantages of load-carrying lattice structures and distinct topological and geometric design to generate integrated kinematic solutions for a wide range of applications such as morphing wings, robotic grippers, and adaptive building facades.