Under Settings -> Lock Screen, the 'Screen times out after' drop down only gives me the option of 5 minutes maximum. I've seen posts online from some people who have similar phones and have the 'never' option in the dropdown. I have a Lumia 820 and I have no password enabled on the lock screen. Is there something that I've overlooked?
Settings > Lock Screen > "Screen times out after" is the only place you can configure the lock screen timeout setting.
The times listed in the dropdown appear to vary by device and firmware version.
For example, I had a lend of a developer Lumia 920 from Nokia and it listed many timeout values including "never". Yet my own Lumia 920 (UK, unlocked) has less timeout options available doesn't include "never".