What exactly is Luneshine?

Solution 1:

Luneshine is not something that needs to be unlocked. You can pickup items with Luneshine.

Luneshine - Luneshine is an additional feature that an item may possess, and can be found on items found throughout the game.

Source

The keyword defined on the wiki just says that Luneshine is an additional feature that an item may possess. I'm assuming the word itself is just a play on the word "Moonshine".

Additionally:

You can get Luneshine on items that you collect from the Grinder. You have a greater chance at success if you use Moonstones when using the Grinder.