So does the live wallpaper still run and use CPU when the phone is locked/asleep ? When I look at the battery usage, in which category does the live wall paper usage fall ?
It shouldn't be running when the screen is off.
Shouldn't being the key word there. If it's wallpaper developed by a 3rd party, there's always the potential for coding issues.
In the battery usage it should be under the Android System usage. Live Wallpaper is an Andorid function rather than a Display function. Display is for the screen brightness, etc. There's no easy way to separate it out. I'd just give it a shot if there's one you like and if your battery drains faster, then you may need to try something else.