Computer-Aided Lift Planning (CALP) systems provide smart and optimal solutions for automatic crane lifting, supported by intelligent decision-making and planning algorithms along with computer graphics and simulations. Re-planning collision-free optimal lifting paths in near real-time is an essential feature for a robotized crane operating in a construction environment that is changing with time. The primary focus of the present research work is to develop a re-planning module for the CALP system designed at Nanyang Technological University. The CALP system employs GPU-based parallelization approach for discrete and continuous collision detection as well as for path planning. Building Information Modeling (BIM) is utilized in the system, and a Single-level Depth Map (SDM) representation is implemented to reduce the huge data set of BIM models for usage in discrete and continuous collision detection. The proposed re-planning module constitutes of a Decision Support System (DSS) and a Path Re-planner (PRP). A novel re-planning decision making algorithm using multilevel 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. Two case studies are carried out with real-world models of a building and a specific tower crane to validate the effective performance of the re-planning module. The results show excellent decision accuracy and near real-time re-planning with high optimality.