I bought these two lamps 10 years ago and the shade is made from paper. They held up just fine before kids, but the kids haven't been too kind with them over the past few years and they had tears in them.
I like the lamps and the shades are an unusual shape, so there wasn't a way for me to find replacements. I opted to recover them myself with a cream colored fabric. You can't tell from the pictures, but it's a diamond design with dots. I measured the shade and cut the fabric out and hemmed the edges.
Next I hot glued it to the lampshade frame.
Then I trimmed the edges with double fold bias tape in a taupe color to give it a bit of contrast.