Question:
I really feel pretty dumb because I have looked at examples but want to be sure with the name of this fabric.
My inclination is to call it damask.....
Answer:
Well, I think it probably is a damask. (Not really a close enough photo to be absolutely sure...) You might also want to use the term 'jaquard weave.'
Not sure if that's the word folks will be looking for when searching for a lampshade, but it sure won't hurt to use it....
Good luck!