A storage system comprises a plurality of storage devices and an associated storage controller. The plurality of storage devices are configured to store a plurality of logical units (LUNs) and snapshot data structures associated with the plurality of LUNs. The storage controller is configured to determine a mapping of a logical address associated with a pending read or write operation to a snapshot address associated with a given snapshot data structure of the storage system that comprises a plurality of nodes generated during point-in-time snapshots taken based on at least one of the LUNs, lock at least a portion of the given snapshot data structure during the read or write operation based on the determined mapping, and release the lock on the at least a portion of the given snapshot data structure in response to a completion of the read or write operation.