فص صفحة (10):
"My brother's the new Lord Burlesdon," I explained. "So, do I really
look like the King?"
I think it must be Lord of Burlesdon

Lord Burlesdon is correct

It`s like Lord Carnarvon - one of the two guys who dicovered Tutankhamun`s tomb

Burlesdon" is a name of someone or a place?
That's the question.

If it is a name of someone ,it is right.If it is a name of a place,it is wrong

Burlesdon refers to the place and the person who governs that place. In Shakespeare`s Macbeth, we had Cawdor (or Lord of Cawdor) , Glamis (or Lord of Glamis), etc. However, In the Prisoner of Zenda, "of" was not used. Lord is also a British title that is inherited and it enables you to be an MP in the House of Lords.
It`s like Pacha in Egypt.
Best Regards

Thanks a lot