Lets say I create a dump of a block device like so
dump -0 -A L0.archive -f L0.dump /dev/sde1
Now in this case sde1 is not mounted, as to not be live. So how can I restore sde1 from the other partition while sde1 is unmounted.
The standard process for restoring from a dump file is to recreate the filesystem (mkfs), then restore into the freshly-created filesystem.
If liveness of the filesystem is a concern (but it's not a critical fs like root, /usr, or /var) then you can mount the new fs away from where something would go looking for it, and remount it at its proper spot once the restore is complete.