Check notifications. The home/lock is shown when a notification is received as it turns on the screen.iOS- rather than model-related, but...
My two daughters both have a 5c. Elder daughter has had hers a year, and it's incrementally reached 9.0.1. Younger daughter has just inherited her mother's two year old 5c and I've set it up from scratch with 9.0.2.
As far as I can tell both iPhones identically configured with regards to everything that impacts on battery life. The girls have very similar usage patterns, and if you look at the battery usage stats everything is broadly the same except for 'Home & Lock Screen': the 9.0.1 is 7% over the last 24 hours (and over the entire week), whereas the 9.0.2 is 22% over the last 24 hours (and 21% over the three days since 'commissioning').
The most obvious explanation is it's a 9.0.2 'feature' (of the 5c, at least) but I can't prove it without updating the 9.0.1 iPhone, which I don't particularly want to do for obvious reasons...
EDIT: or rather than being a 9.0.1/9.0.2 difference, it's down to incremental installs from 7.1.x onwards vs fresh 9.0.2 install.
You can either go nuclear and turn off notifications for each app or disable the show on lock screen so it wont wake up the phone.