A Lift Planning System (LPS) is an imperative component for optimal and safe autonomous crane lifting,  possessing the ability to plan collision-free optimal lifting paths in complex construction environments. In real-world construction sites, there are multiple objects (equipment moved by construction workers, vehicles, other cranes etc.) in the scene which may shift their position after the initial lifting plan for a building component has been prepared. This work on path-replanning involves making decisions on re-generating portions of an already planned lifting path in the presence of dynamic objects in the construction scene and strategizing the implementation of that decision. The application is exclusive to tower crane operations in residential or non-residential building construction. Building environments from Building Information Modeling (BIM) systems are utilized in the LPS. Dynamic objects in the scene, considered obstacles, are classified according to their effect on the planned lifting path. The obstacles are updated to the original Single-level Depth Map (SDM) of the environment via an SDM integration technique to portray the dynamic nature of the construction scene. Following the obstacle modelling, a re-planning module constituting a Decision Support System (DSS) and a Path Re-planner (PRP) is prepared. A novel re-planning decision-making algorithm using multi-level Oriented Bounding Boxes (OBBs) is formulated for the DSS. A path re-planning strategy via updating the start configuration for the local path is devised for the PRP. Experiments with scaled real-world models of a building and a specific tower crane show excellent decision accuracy and near real-time re-planning with high optimality.