Sync your back up drive/folders to the main drive and you're sorted. Lots and lots of software that can do that for you.
Yes, this isn't really something LR can do - not safely. It's something you have to arrange in conjunction with your backup software. Loads of stuff does that. I use the Microsoft utility Robocopy. Look for something that can do mirror copies or synchronised copies.
Note that this sort of thing is a bit dangerous if you don't have a multi-copy backup system, or some archive system. Otherwise, the moment you mistakenly delete a file, it's also gone from your backup!