Although robotic spatial printing (RSP) has demonstrated a new way of fabricating building components with a good stiffness-to-weight ratio, the complexity of the applied geometries is still limited. Among them are branching geometries, which refer to the bio-inspired branching structures (BIBSs) in the building industry. This paper presents a cutting-edge approach to tackle this bottleneck problem, in which we propose an automated printing path generation (APPG) approach for the RSP of branching geometries, including an original hierarchical framework of printing node permutations and a linear workflow that incorporates five core algorithms: the heat method, graph generation, graph traversal, curve adjustment, and lattice generation. Through the execution of this workflow, a lattice structure and its corresponding printing path can be generated. This work is validated by the simulation of three prototypes: two-branch geometry, multi-branch geometry, and multi-level-branch geometry. Printing expenses are compared with each of the related algorithms to validate the efficiency of this proposed approach. Along with the appropriate APPG solutions, an analytical tool for topological type is also presented in this paper.