Google Issue 165558 : Workaround
As reported a lot of people have a very poor battery life on Lollipop.
I had the issues, but found some settings you can change to get better battery life.
These changes worked for me, you'll have to check for yourself if they help or not.
Switched 4G to 3G
Blocked Wakelock *alarm* and *net_scheduler* (root needed)
Switched Location to GPS (Device) only
Disabled Google Location Timeline
Also the information provided by Lollipop seems to be really buggy,
it shows different information on the same day without charging. 81% => 12h left 76% => 19h left 74% => 23h left
See Screenshots below.