An apparatus comprises a processing device configured to identify a snapshot lineage comprising snapshots of a given storage volume, the snapshot lineage comprising (i) a local snapshot lineage stored on a storage system and (ii) a cloud snapshot lineage stored on cloud storage of at least one cloud external to the storage system, the cloud snapshot lineage comprising at least a subset of the snapshots of the given storage volume. The processing device is also configured to determine whether the local snapshot lineage is associated with any current local storage volume of the storage system corresponding to the given storage volume and, responsive to determining that the storage system is not associated with any current local storage volume corresponding to the given storage volume, to select a snapshot from the cloud snapshot lineage and recover the selected snapshot to a new local storage volume on the storage system.