There is a theme of immortality that runs throughout "Song of Myself" as the speaker discusses life and death as a cycle. If you review Section 6, you will see at the end where the speaker discusses the question of what happens to people after death in relationship to life.
In talking about the "dead young men and women" the speaker says:
They are alive and well somewhere,
The smallest sprout shows there is really no death,
And if ever there was it led forward life, and does not wait at the
end to arrest it,
And ceas'd the moment life appear'd.
All goes onward and outward, nothing collapses,
And to die is different from what any one supposed, and luckier.
Remember that Whitman was alive and wrote during the transitional time from romanticism (and transcendentalism) to realism. In a way, his assertions could be looked at as a view of death from both a natural (and therefore romantic) standpoint as well as a scientific/realistic standpoint. If nothing else, he acknowledges that life and death are part of the same cycle. In comparing death to life, here, the speaker explains death does not really exist because ultimately it leads to a rebirth of something else. This second chance is what the speaker means when he says death is "different" and "luckier" than what most always considered it.