Life and Non Death

In the prayer for rain we entreat “For life (lechayim) and not for death (lamavet).” The Shulchan Aruch, states that one should be careful to say “lechayim” and not “lachayim,” which would mean “not alive” (“lo chayim”). If so, why do we say “lamavet,” which implies that we seek “life” and not “not-death”?

Rabbi Levi Yitzchak, the Rebbe’s father, explains that we pray that we will have true life, and not merely “non-death.” (According to Tradition)