In the very, extremely, never-happened-and-hopefully-never-does event that your LuckNews database becomes corrupt, you will still have access to all your subscriptions. The time and effort you have spent building a list of subscriptions is important and LuckNews goes an extra step to try to ensure that they are always available to you.
These files are really created as an extreme fallback measure - accessing them is a little tedious.
The backup files are stored in a directory deep in your hidden 'Library' directory. To access it, you can try one of two methods:
1) In the finder, open the 'Go' menu and hold down the option key. Holding down the option key will cause the 'Library' folder to be shown. Click on the Library folder. You now need to navigate to the folder where the database and OPML files are located:
~/Library/Containers/com.craigmcpheeters.LuckNews/Data/Library/Application Support/com.craigmcpheeters.LuckNews/2) The second way of getting to the proper folder is to, again, go to the Finder and open the 'Go' menu and select the 'Go to Folder…' menu item. When it asks for a path, cut and paste the path above.
Sorry about the path being so long. I really don't expect anybody to ever need this capability - but I hope you feel more confident in the application knowing they are there.
Once you have the proper folder open, you will see up to 10 OPML files. If you have the finder sort these files by date modified (by clicking on the 'Date Modified' title) you will be able to see which of these files is the most recent. Depending on what you want, you may want the most recent file, or the previous one, or its previous, etc. Click and drag the OPML files you want to your desktop. Once that is done, import this file in LuckNews (via the File menu's item: Import Subscriptions…)