Can you recover it with new fabric?

Here's a tutorial that might help: https://www.youtube.com/watch?v=SkrYoLPZGqY

If that particular tutorial won't help, you could try using Mod Podge for fabric to adhere a new layer of fabric over the old one and shape it however it needs to be shaped.

Madeline: these should be helpful!

https://www.thespruce.com/how-to-paint-a-lampshade-4587801

https://www.marthastewart.com/911978/how-paint-lampshade

If you want to just clean it, I would try using a granular hydrogen peroxide product like Oxyclean, you can find an equivalent of this at dollar tree, I would soak the shade in it if you think the shade fabric can withstand that. After soaking I would clean it gently it with blue dawn dish soap in warm sudsy water and a micro fiber cloth and rinse, let it air dry.

Best to you.

Here are some ideas from other HomeTalkers

https://www.hometalk.com/search/posts?filter=lampshade

https://www.hometalk.com/search/posts?filter=cover%20lampshade

https://www.hometalk.com/44263857/update-and-old-lamp-shade-with-these-simple-steps

https://www.hometalk.com/43854244/using-jewelry-to-refresh-thrifted-lamps

Update an Old Lamp Shade With These Simple Steps

Using Jewelry to Refresh Thrifted Lamps

Can you cut off the cloth, trace the shape on new cloth, and reattach it? Or you could try painting it? https://www.hometalk.com/41925921/learn-how-to-paint-a-lamp-shade

Learn How to Paint a Lamp Shade

Hello I have spray-painted both fabric lampshades and paper lampshades. Covering with fabric might be the most elegant choice though. I have even seen bloggers wrap lacy strips around lampshades —it all depends on your decor aesthetic.

I hope you find the perfect solution to upscale your shade..

Paint, removable wallpaper, take off the existing cover and go industrial with the metal frame, farmhouse chic by adding chicken wire, or a bit of lace to soften the look.

You could spray paint it or stencil it

Madeline...If it does not have any damage I would use spray paint. I have one I sprayed a number of years ago and I still use it.