Data migration is performed in a cluster of host computers each using a mechanism associating data with a source LUN. During a synchronization operation the contents of the source LUN are copied to the target LUN while ongoing normal source LUN writes are cloned to the target LUN. A datapath component of an agent coordinates the writes at the target LUN to maintain data consistency. Upon completion of synchronization, each host stops the write cloning and disables access to the source LUN, in conjunction with a modification of the mechanism to newly associate the data with the target LUN. Depending on the type of mechanism and system, the modification may be done either disruptively or non-disruptively, i.e., with or without stopping normal operation of software of the host computers.