Robot manipulation of Deformable Linear Objects (DLOs) in tasks such as Shoe Lacing (SL) is challenging due to the objects' high dimensionality. One of the key components to successful manipulation is accurate state estimation. Existing methods focus on the DLO itself without considering the interaction with the scene objects. The estimated DLO relation with the scene objects is an important factor in task planning. In SL, the shoelace and shoe relation decides whether the shoelace should be inserted, and the target eyelet for insertion. In this work, we propose an algorithm, Tracking for Shoe Lacing (TSL), which combines probabilistic registration with physical simulation, to preserve the topological relations between the shoelace and the shoe. Leveraging the physical simulation, it also identifies system anomalies during the tracking process. We propose two evaluation metrics: Sequential H-Signature, which qualitatively describes the shoelace-shoe relation to assess algorithm performance, and Dynamic Time Warping (DTW) distance, which quantitatively evaluates tracking errors against the groundtruth. The result shows that TSL achieves tracking error on a par with the state-of-the-art algorithm, and it is the only method that correctly estimates the shoelace-shoe relations across all experimental conditions.