There are many reasons you can lose an OnSong library including deleting the app and reinstalling it, problems with an iOS update, or an issue with the OnSong library itself.
You can start by going into OnSong > Tap Songs > All Songs > Books > Back > Select Default Library and see if that restores your songs.
If that doesn't work, tap the Utilities menu (gear icon) in OnSong and then choose Tools and then Fix Library. If there is a problem with your library, OnSong will prompt you to correct the problem. If you agree, this should restore your library.
OnSong stores your library of songs on your device. We recommend that you backup your device to iTunes or iCloud in case your device is ever lost, stolen, or damaged. You can learn more about backing up your device here: https://support.apple.com/en-us/HT203977
One issue with this is restoring a backup requires a fresh device since all information will be replaced. The other issue is that it may not contain the OnSong library you need. For these reasons, we recommend that you backup your OnSong library to ensure you can get up and running in any event: http://onsongapp.com/videos/tutorials/backup/