I can think of a "cheater method" that would be much easier than coding but could solve your issue depending on the purpose. (If your "end goal" is to be able to "time things" without unlocking your phone this could suffice.)
You could create an Animated GIF for your lock screen image, showing the seconds counting (or optionally higher resolution like tenths of a second) in digital, analog or whatever other format you wanted.
With a jailbroken iPhone you can use an app like GifLock to use an Animated GIF for your lock screen image. (Source)
With a non-jailbroken iPhone I think you can use an app like Giphy to convert an Animated GIF into a Live Photo which can be set as a lock screen image. (Source)
As for creating the Animated GIF to your liking, I use ScreenToGIF for all my GIF-animating needs. It's meant for PC screen recording, so this wouldn't be within it's "intended purpose", but outside of that there are numerous tools for building Animated GIF's.
I slapped this together in 2 minutes for testing at my cell's resolution.
(Obviously you would need to include more than 4 frames.)
Image from one of the links: (It made me LOL so I had to include it)
...and just since we're on the topic of Clocks & GIF's, here's one I just added to my SO profile page, for no constructive purpose whatsoever:

(Click the image to view a mesmerizing 'large version' while you ponder your lock screen options.)
PS - I realize this isn't solution isn't following the criteria set in the question and therefore I don't expect the bounty. Honestly I didn't even realize there was a bounty until just now, I'm just trying to think out-of-box for alternative solutions.