If the light is double insulated it should not be earthed.
I never cease to wonder why the wording is "should not be earthed" instead of "need not be earthed".
The only apparent logical reason is that not earthing the item prevents it being the return path for an electric shock from some other source.
In this lamp perhaps the case is not earthed to prevent shock to a person who, while changing a lamp, touches a live part and the frame at the same time.
If it is so old that it is not marked with a DI symbol AND it does not have an earth terminal then it should not be used.
Agree with that for items as found.
But where items can be modified to provide reliable and assured earth continuity to all exposed conductive parts then they could be safe to use.