Over on the Android Developer Preview portal, Google has acknowledged an issue with battery life on Lollipop.
The problem occurs when a device running either 5.0 or 5.1 uses data. Internet apps will continue to drain the battery by keeping mobile data active unless they are forced to stop. On KitKat, apps stop doing so once they have completed their tasks. According to the user who reported it, this happens on Android M, as well. He or she also adds that the issue has been in the Android Issue Tracker since April, but Google has given it low priority.
A project member responded to the post with this:
Thank you for reporting this issue. We have passed this on to the development team and will update this issue with more information as it becomes available.
Personally, I’ve experienced this since my LG G3 updated to Lollipop some time ago. Battery life indeed was worse, as the personal anecdotes I had read had mentioned.
Still, Google realizes this complication, and hopefully, this means that Google will raise its priority and work to fix it, especially as Lollipop (and later, Android M) becomes the most used flavor of Android.