Backup files from an application for which I forgot unlock pattern
Accessing the files in the app's protected storage directory will not be possible without root because you will not have proper permissions to access the directories. If the app saved any data to external storage (SD card, for example) then you can get it, but not knowing the app in question it's hard to say where it would be. Generally speaking it would likely live in /sdcard/Android/data somewhere assuming the standard APIs are used, but it doesn't have to use that directory.