DISCLAIMER: Copied from [https://raspberrypi.stackexchange.com/questions/85958/easy-backups-and-snapshots-of-a-running-system-with-lvm/85959]
Moving the installation isn't the problem but the LVM drivers must be loaded on boot up so the root partition can be mounted and used for booting. Fortunately the Raspberry Pi supports loading a ramdisk for initrd so we have to do an additional step to create the initram containing drivers for LVM.
The following is only for a quick setup an initramfs where you have to monitor kernel updates by yourself. To use a more automated setup an initramfs you can look at How can I use an init ramdisk (initramfs) on boot up Raspberry Pi?.
If you are unexperienced with linux please try it first with a new image how I did for this How To. You can loose all data.
For reference I use Raspbian Buster with Desktop 2020-02-13, flashed it to a SD Card and boot it in a RasPi. First do an upgrade to get the latest software versions and instal
