First, congratulations on your new Livin' Lite- my dream trailer! It's rough to have any problems at all with a new rig, so sure understand your concern there...but if it's any comfort, this problem isn't related to its construction, so no worries there, right?
The "E3" error code on a Dometic may be a real simple fix. I THINK there's a red "reset" button on the back of that fridge. If it's there, it may need to be reset....
If that doesn't work, I'm sure others will have suggestions- and if NOTHING works, I'm betting that Camplite will step right up, even though appliances are usually covered by their various mfr's. They have a very good customer service rep, and want to keep it.
Good luck!