Settings>Display>screen timeout seems to only work for the device when you get past the lock screen.Settings>security>Lock Automatically doesn't seem to be an option,at least not on my version of the phone.
No matter what the screen timeout is set to my lock screen will go dark after about 5 seconds.The exception is when you have it plugged in.It will stay lit.With at least one lock screen customization tool available that I know of,it would seem odd if it were not possible to change this.If you customize a lock screen,you probably want to spend some time viewing it.
I'm thinking mihqke might be correct that there's no stock provision for changing the lock screen time out.If some app might include this ability,I'd like to know before paying for it.Thanks for both of your responses.