There is nowhere for you to add an earth as the cable goes right into the switched lamp holder. The only way to earth would be to replace it with a metal one. If you were thinking of taking a cable out of the plastic lamp holder and to the chassis of the shade then you would be modifying that holder which is something that you shouldnt.

If the cable goes into the base of the lamp and has a switch or something then that should be earthed. But if the wire is straight from that lamp holder to a plug then nothing to earth as once that cable is replaced, its all double insulated. That lampholder may not meet standards for disassembly without tools that is now required tho, as the back looks to just screw onto it by hand.

RC: I had this old topic reopened as I have a couple of old NZ lamps id like to rewire & I wanted to query adding a connection from ground to the metal lamp base.

A member of Nz Vintage Hifi Facebook group who repairs hifi gear warns against adding ground to non-grounded unshielded lamps:

Grounding a lampshade exchanges one potential hazard for another as it introduces the possibility of receiving a strong electric shock as you hold the lampshade with one hand and reach in with the other to extract a broken bulb or a blown one which breaks during removal. You get the shock across your chest.
…
Check the wire connections to the rear of the lamp holder and if all is well it can be left alone … the insulation might have hardened near the end because of years of heating by the bulb - in which case you just cut it back then reconnect.

Hope this helps someone else.