License files can be found in the Application Support folders that you’ll find in
- For PhotoLab 1 … 7 → /Library/
- For PhotoLab 7 … 8 → /Users/…/Library/
You should be able to restore the license files from a backup, provided you have one and you’re restoring to the same Mac that you used to activate PhotoLab.
Note that there is some overlap with PhotoLab 7. As long as you have either of the license files, you should be able to make PL7 work again. All other versions need the files in the proper locations.
Please also check for *.lock files as noted here: