OK. Is the lampshade all plastic?
If so you don't need to earth it, if it's a metal (or partially metal) shade then I'd attach the earth somehow.
The shade isn't conductive but the bulb mount / hanger is metal and could be low enough to be grabbed.
If the fixture was designed as a Class II then you don't need to worry about it. Is there a symbol on it the looks like this?
@Howard started
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OK. Is the lampshade all plastic?
If so you don't need to earth it, if it's a metal (or partially metal) shade then I'd attach the earth somehow.