I was invited to visit the Delta One @ LAX check-in area today...
I'll try to revise this post with photos shortly, but the links already posted do a great job of showing the space. It's not huge, it's not meant to be a lounge, rather a calm and discreet place to handle check-in formalities.
It's not the same snacks at the Sky Club as its intended to just be a refreshment and healthy snack before you head to the Sky Club or directly to your seat onboard. There is no booze.
I think Delta has done a great job with this.