In the statics "Person who lived the longest", is it correct that the person has to be death??
My aunt is far away the longest living person in the familiy and still alive, but is not recorded in the "statics"
Yes that is correct. That is, at least in English, clear from the use of the word "lived" which is past-tense and therefore indicates that the person is no longer living.
There is a separate statistic on Menu > Charts > Statistics > Individuals tab that is titled "Oldest living people". That will show your Aunt (but of course only to those users you allow to access data of living people.