We devise, implement, and benchmark a framework LUKIS to automate the process of geometric digital twinning for existing slab and beam-and-slab bridges. LUKIS follows a top-down strategy to detect and twin bridge concrete elements in point clouds into an established data format Industry Foundation Classes. Existing software packages require modellers to spend many labour hours in generating shapes to fit point cloud sub-parts. Previous methods can generate surface primitives combined with rule-based classification to produce cuboid and cylinder models. While these methods work well in synthetic datasets or simplified cases, they encounter challenges when dealing with real-world point clouds. We tackle this challenge by investigating the entire workflow of geometric digital twinning for bridges and proposing LUKIS to auto-generate bridge objects without needing to generate low-level surface primitives. We implement LUKIS on a single software platform. Experiments demonstrate its ability to rapidly twin geometric bridge concrete elements. Compared to manual operation, LUKIS reduces the overall twinning time by at least 95.4% while the twinning quality (spatial accuracy) is improved. It is the first framework of its kind to achieve the geometric digital twinning for primary concrete elements of bridges on one platform. It lays foundations for researchers to generate semantically enriched digital twins.