Raspberry Pi as a backup server
It is possible to use a Rasberry Pi as a backup server. They may be used to pull or push backs. Please see the appropriate page(s) relating to the advantages of pull backups. Given the price points and low power requirements and small form factors, there are many reasons for using a Rasberry Pi as a backup server particularly for geo redundancy.
Powering the Rasberry Pi
Because, the many Rasberry Pi units simply run via USB there are many options for power both on and off grid and in terms of a UPS on a budget and in size, something like the Voltaic Systems V44 can be a great option to ensure the system continues to run during a short power interruptions.
Pushing Backups
Using the in-build example post action scripts it is easy to push a backup (made to a disk image bundle) to a remote server to which you have SSH access. The advantage of this approach is that data at reset is easily able to be encrypted and all meta-data is easily saved. By making use of a disk image bundle, it is possible to just sync the changed chunks to the server.
Pulling Backups
This is the default approach for backups with LBackup. However, in addition to running Lbackup on the remote system you could also run a separate script or backup package to pull an Lbackup disk image bundle. The main thing to bear in mind is to make use of the lock files to ensure that LBackup will not activate and update the disk image during the pull to your Raspberry Pi.