I think you are confusing the 'act' or process of dying with being dead. And the death of the sinner does not produce forgiveness by God. Without an arrangement for forgiveness (Jesus' sacrifice) the sinner would simply stay dead. Thus, when Lazarus was brought back he was still a sinner and destined to eventually die.
Part of the WT's mistake is embodied in their translation of Romans 6:7 -
For the one who has died has been acquitted from his sin (Rom 6:7 rNWT)
The error is the inserted word "his." It does not belong in the text. Romans chapter six is comparing baptism to death. The writer is saying that when a person dies they are no longer subject to the desires that produce sin - because they are dead. "Acquitted," in this context, would more properly be rendered "set free."