One of Morrie's "lessons" is that one is responsible for creating their own "culture." He means that our choices can either make our lives nourishing and rewarding, or toxic and unproductive. Although Morrie is facing a terrible, debilitating illness, he decides that he will use his situation to teach about the process of dying. He is "lucky" in the sense that he has this opportunity and the courage to embrace it.
Morrie also considers himself lucky to have foreknowledge of his death. This gives him the opportunity to "say good-bye" to loved ones. For many, death comes suddenly or violently. Morrie is lucky, for example, to have a chance to reconnect with his former student after so many years. He is lucky to have the foresight to have a kind of "living" funeral, in which he can share his love with his family and friends. Most of all, he is lucky to be able to give to others. His illness has made this sort of giving easier, in a way, because his sense of the closeness of death removes inhibitions and makes talking directly with people easier; the hardest thing about his illness, he says, will be when he loses the use of his hands and voice, because that is how he connects to others.