The rich man also died and was buried. Jesus clearly tells us that we exist after death. This verse is showing that God is presently the God of Abraham. Man is mortal by nature not immortal. God alone has immortality.
Man is subject to death because of sin.
For the wages of sin is death . . Immortality is a gift of God bestowed on His followers alone. Man is not immortal he is subject to death becuase of sin. I will later respond with more information on the nature of man. Time right now does not permit me to go any further.