Could I add a lining after-the-fact?

After making my most recent everyday skirt, (and literally, wearing it everyday this last week!) I think I might prefer it with a lining. Is it possible to add one after I've already made the skirt? Has anyone done something so nutty before? And, what fabric would you recommend? The skirt is made of a linen that is dark brown with a thin black pinstripe so I wouldn't want anything light in color, but I do want it light to the touch.