I have an Ubuntu installation using LVM and LUKS encryption. LVM and encryption were chosen during the install process).
While logged into it, I backup the full live system using rsync to another drive. If I ever have to restore the full system to a new hard drive, I would boot with the Ubuntu live CD and reverse the rsync command to restore everything to the new drive, and I'll fix grub and fstab. My newly restored system will work, however, this will not restore LVM or LUKS so the restored system is without these.
I was thinking, in order to keep LUKS and LVM, can I first install a fresh install of Ubuntu onto the new drive with LUKS and LVM during it's setup process, and then restore using rsync over the fresh install after mounting it in the live CD environment?
--one-file-system
, your backup is likely incomplete.