An apparatus comprises at least one processing device configured to select a snapshot lineage comprising one or more snapshots of a storage volume comprising data stored on one or more storage devices of a storage system, the snapshot lineage comprising at least one cloud snapshot lineage, the at least one cloud snapshot lineage comprising at least a subset of the one or more snapshots of the storage volume that have been copied to cloud storage of at least one cloud external to the storage system. The at least one processing device is also configured to generate configuration data for accessing the at least one cloud snapshot lineage. The at least one processing device is further configured to transfer the configuration data to at least one additional processing device to enable the at least one additional processing device to access the at least one cloud snapshot lineage.