While there is a KB for this, I had to whitelist a specific folder in order for the backup to work. The moment the backups started failing was the same day I implemented Lockdown on one server. Once I whitelisted the folder below and re-ran the backup it was successful.
Original KB: https://community.sophos.com/kb/en-us/133231
The Veeam backup error I was receiving stated:
What to do
1. Login to your Central Dashboard.
2. Navigate to Server Protection > Policies.
3. Open the Lockdown Policy which is applicable on the server where the backup is failing.
4. In the Settings tab, click Add allowed file/folder.
5. Enter in the following exclusion:
6. Click Save.
Run the backup again and it should be successful.