Time Expanded Networks, built by considering the vertices of a base network over some time space, are powerful tools for the formulation of problems that simultaneously involve resource assignment and scheduling. Still, in most cases, deriving algorithms from those formulations is difficult, due to both the size of the resulting models and the propagation of time rounding errors. The purpose of this paper is to address this algorithmic issue. We propose a generic Project and Lift decomposition scheme, and focus, inside this decomposition scheme, on the Lift issue, which consists in turning a solution defined on the base network into a solution in the time expanded space.