Will Lightning 1.03 work with Drupal 8.2.x?
Does lightning have a branch for Drupal 8.2.x?
Yes. 8.2.x-1.x is our Drupal 8.2.x dev branch. It will be released 6 OCT - at the same time as Drupal 8.2.x.
Is packagist aware of the 8.2.x-1.x branch?
No. It's only on github. So you would need to define the github VCS in your repositories key in you composer.json (or build from the Lightning GH repo directly).
What is the 8.x-2.x branch on D.O?
That's used for testing the D.O packager and should not be used.
Is there a branch named 8.1.x?
No. Packagist translates 8.x-1.x to 8.1.x and gives you the option of referring to it as either dev-8.x-1.x or 8.1.x-dev.