What you need is instead of:
+ **/radarr/Backups/**
- **/radarr/**
+ **/sonarr/Backups/**
- **/sonarr/**
+ **/lidarr/Backups/**
use
+ **radarr/Backups/**
- **radarr/**
+ **sonarr/Backups/**
- **sonarr/**
+ **lidarr/Backups/**
to make it work for your both sync commands.
Potential problem is that these patters can match different items than intended. You could see unexpected example in case of "QDirStat". To do this right you have to create more complex filters using regular expressions.
But IMO more complex you make it then more likely you will create bugs and make mistakes. Keep it simple. I think I would rethink my script or use two different filter files with very explicit rules.