Hierarchies are fundamental structures across various disciplines, modelling hierarchical relationships in computer science, biology, social networks, and logistics. However, dynamic and concurrent updates in real-world systems necessitate synchronisation techniques for maintaining data consistency despite concurrent access. This paper explores a novel approach called CALock to synchronise operations on hierarchies by utilising a labelling scheme that facilitates multi-granularity locking. Our approach addresses both concurrent data reads and writes as well as structural modifications. CALock exploits the hierarchical topology via a new labelling scheme to identify the common ancestors of vertices. This enables a thread to identify an appropriate lock granule for its lock request. Leveraging variable lock granularity optimises operations across the hierarchy while ensuring consistency and performance. We provide a detailed discussion of the CALock labelling and the locking algorithm, prove its properties, and evaluate it experimentally. CALock remains competitive with previous labelling schemes on static hierarchies and has better concurrency and throughput when structural modifications change the hierarchy. In particular, CALock improves throughput by up to 4.5 times and lock response time by up to 1.5 times for workloads that contain structural modifications.