There are many solutions for Computer/Server backups. One that I use right from Lightroom is that I run a NAS (Network Attached Storage) that is in RAID 5 where Lightroom backs up its catalog and imports photos to both my computer and the NAS as the same time.

Other solutions that you can get are looking into backup software that backs up your data to multiple locations. You can backup to cloud, disk, and tape.

If you are looking for a Windows-only-based backup that is more for a small office or business, you can look up at Veritas BackupExec. if you are looking for Enterprise backup solution, Veritas Netbackup, CommVault Simpana, etc.

Mac has TimeMachine for end users but it's not as robust as the more dedicated software. Windows does have the Windows backup but I have never seen anybody actually use it.

When looking to back stuff up, you always have to look at it from an OS standpoint vs. an application standpoint. It will make your solution for restoring easier.

Edit:.

For having the photos save to a network device and your local drive at the same time, you need to map the network location to a network drive in windows or in mac, mount the location and save it in the fstab file (unix system file).

Once the drive is mounted to a network drive / folder path, in Lightroom, click import, and on the right side of the import menu under File Handling, there is an option to "make a second copy to" and you click the drop down menu and choose a folder. If you choose the mapped network drive or mounted path (mac), it will save a copy to the network device that is mapped to it.