When you're done with the Gospel Library, are you going back to the library home page and then tapping the Android back button? Or do you just hit the Android home button or something similar? Cuz I haven't seen the Gospel Library open itself, so I'm wondering whether your Android is actually closing the app. Do you have one of those widgets that shows open apps so you can verify it closes (or doesn't) when you think you've closed it?
If it's not closing, I would use the feedback in the app to let the developers know as it's probably device-specific (I know it closes on both of my devices).
I've looked all through the settings and cannot find one that looks like it would re-open the app. Are you by chance using the bookmark widget? (I don't, and I'm wondering if maybe that keeps something open.)
Also, are we talking about a phone or a tablet? If a phone, have you told it to only update over WiFi? (That might help, not sure.)
Finally, if you haven't already done this since the lollipop update, you could try clearing the cache for the app (not the data, unless you want to re-download everything), then powering off the device for a minute or two and powering it back up? I've read where some people had to do a factory reset, apply any other device updates, then reinstall all their apps and restore all their data, and then their "lollipop" battery problems were solved (seems drastic, and I haven't needed to do that, but that's something I've read).
Just some random thoughts while waiting to see if anyone else has seen this.
Liz