How to stuff Brown Sugar croissants?

Since you haven't provided any additional information, I'm just going to provide our best guess here, what SAJ14SAJ and I were both thinking.

If you want to put something in a croissant, whether it's a piece of chocolate or any other filling, the normal way is to put a strip of it along the side of the triangle which becomes the inside of the croissant. That way it gets completely surrounded when you roll it up and has no effect on the croissant holding together. This should work just fine for brown sugar. Just make sure not to go all the way out to the ends, or it may melt and seep out as you bake.

From the little you said, the hardening up with butter or lard sounds like it's just a way to crisp up the outside. (Brushing with butter is a technique not limited to croissants.)

And finally, a wild guess, based on your crude translation: "lip" as in "projecting opening" (like perhaps the lip of a container) can be translated to "bord" or "rebord" in French; if your recipe said one of those, a better translation would be "edge" or "side", which is entirely consistent with what I said above.