When two things have a life-time of correlation, it means that they have been connected or related to each other over a long period of time. For example, let's say your parents have been married for a long time. That means they have had a life-time of correlation, because they have been related to each other for a long time. That's the same idea with things like temperature and humidity being related or correlated - they have usually been connected or related to each other for a long time.