The Queen Mother wrote:In good times and bad she never lost her capacity
to smile and laugh nor to inspire others with her warmth and kindness.
The Queen Mother was using a double negative: "never . . . nor," which is technically an error. However, it is not uncommonly used, and especially among the speakers of British English. An American grammarian would have an hysterical fit--known these days as a "hyssie fit," but it is only a minor fault. It was not until the 17th century, after the time of Shakespeare that authoritarian types said we must never use multiple negatives, which are common, and even required in other European languages.
Technically, it should read: ". . . never lost her capacity to smile and laugh
or to inspire others . . . " The meaning is that Diana never lost her capacity to smile and laugh, and never lost her capacity to inspire others.