Most commercially available lady's kilt skirts are machine stitched, and have no lining. They also will have thinner leather straps that attach to a wide waist band that I suspect has some kind of heavy interfacing. I've never taken one apart.

When I make a kilted skirt for a lady, though, I make it more or less like I do men's kilts. I hand sew them, and they are fully lined. I may or may not use a thinner leather strap depending on her wishes and what I have available. Generally I'll have it close opposite of a man's kilt as that is the normal fashion, but I've had requests to have the skirt close on the right, and that's fine.

Really, the question is how does she want it made?