I noticed my Poweramp App (mp3 player) cuts off/shuts off when my phone goes into sleep mode (usually about 5 minutes before it locks up). I do have the latest version of Android Lollipop installed and not sure if that's what is cutting it off (didn't happen in the previous version of Android) OR if it's something like my DU Battery Saver App???
 
I did look into all the available options within DU Battery Saver as well as Googled it, but couldn't quite find a solution to enable Poweramp in the settings. Very annoying when I'm listening to a song and then it shuts/cuts off when the phone goes into sleep mode.

Lucky you.  Since my phone "upgraded" itself to Lollipop, my internet keeps stopping, my emails only update once in a while and I get some weird behavior with the screen state (like going dark when I mute a phone call).
 
Progress.  *Sigh...*

I can recommend using the Clean Master App (free) as it does keep my Android running smoothly (also cleans/clears junk files/cache associated with Hotmail/Outlook). The only odd behaviour I've noticed is my WiFi at home keeps dropping out regularly or get's poor connection.......I'm stil looking into this.
 
Other than those 2 issues, Lollipop has been (on the most part) pretty good for me.

Hmm... I've had the same issues with my home WiFi. Naturally, I blamed Comcast.  Heh.

After Lollipop I want to smash my phone on a hard concrete floor. It is completely useless.
This was the "best" phone I ever had.
Now, it constantly drops wifi and data connections, the battery lasts about a quarter of the amount of time that it used to. At random times my phone mysteriously goes to 3,000 degrees in my pocket. Sending a text is an absurd idea because it ain't gonna happen. Too many buttons and features were changed to who knows what. I can't get pictures to turn side-ways on my phone. Well, it works and then it doesn't.
Other than the previously mentioned items, I think the update went swimmingly.

This is a case where upgrading worked against me. My lollipop was sour apple flavoured. They put out a point release but it didn't help much. My main issue has been screen graphics corruption and a weird blackout mode that requires a reset to clear.