Do post a picture or two of the lampshade frame.
I would consider covering a paper shade with paper or fabric using a spray adhesive. Spray painting could be easier.
I wrapped my shade in twisted sisal rope I glued on with a hot glue gun. I purchased the rope from Home Depot. It was an inexpensive, simple and quite fashionable fix since that look is in style. Home Depot has several different widths and shades.
Remove the lamp shade. Take it apart and use the current fabric as a pattern.
There are lots of ways depending on the style you want! Here's one idea: