Q:

How to backup Debian with encrypted LVM with rsync?

I'm running Debian 9.1 with KDE with full disk encryption and would like to do a backup of the entire drive (including the separate /home partition) using rsync in a way that allows me to restore the system at failure.
How can I do that? What do I need to pay attention to for backuping when my hard drive is encrypted?
(For example do I need to have the drive I backup to formatted in a specific way?)

A:

You have to define failure. Possible options include

Some partitions (e.g.: /boot or /) have missing/invalid data which prevents the system from booting 
Some partitions (e.g.: /boot or /) are corrupted/unmountable
You forgot the encryption password
The entire disk failed
The bootloader is corrupted

The Debian installation media offers useful recovery options.

You can provide your password and mount the encrypted partitions which survived failure. From there you can restore the data you backed up with rsync. This is useful to recover from 1.
You can re-partition your disk. This includes creating new encrypted partitions, possibly with different passwords. Once this is done you can restore the data you backed up with rsync. You need to make sure the partition table and LVM match the original. This is useful to recover from 2, 3, or 4 after replacing the drive.
You can fix the bootloader. If nothing else failed you don't need to restore data.

TL;DR: No specific precautions are required. If you want to rely on rsync alone make sure you can recreate the partitions if you have to, but this is not specific to using encryption. Other options include

Backing up the entire disk (not using rsync). This requires more space and time for each backup, but makes it easier and faster to restore. It won't save you if you forget the password.
Accepting to reinstall the system and only restore the data (not the programs) in case of issues.

