Backup of fulls to a separate remote storage is not easy with Linux LVM alone. More realistic is LVM snapshots copied somewhere else via some other backup agent.
Let's assume the restore design calls for a block level full copy, independent of the original volume group or its member physical volumes. Snapshots are easy to do, but depend on the source VG and do not meet that requirement. LVM can mirror and split volumes, but the procedure would be more involved.
While these features enable use cases like migrations of primary storage, they are relatively advanced, with fewer examples. Further, it may be tricky to present backup block devices to the host being backed up.
As extra block layer features, LVM itself does not provide access to remote storage. Sure, with a suitable SAN you can access a shared storage array, via fiber channel or iSCSI. These LUNs can be used as LVM PVs. Operationally challenging to do so, as many use cases don't use such SANs, operating system install on local storage, for example. And such SANs tend to be short distance and intolerant of loss. Inserting a mirror into protection storage for everything could make for extreme performance demands to keep up with writes to the primary.
More common is copying snapshots with some other tool. Snapshot the source LV. Create VGs and LVs on the separate protection storage. Either do a block based backup like with dd over ssh, or mount the snapshot and do file based backups. Delete the snapshot LV.