The secret to understanding this pericope is to hear it in the context of all the scriptures.
There are always those who want to condemn the rich on the basis of this. Of course, the rich are sinners (like every other man) but Abraham was rich (Gen. 13.2), as was David (I Chron. 29.28) and Lydia (Acts 16.14) was a prosperous merchant. The problem is not that the rich man was rich; the problem was that he did not love God.
We know this because of his failure to love Lazarus. He did not heed the 5th commandment, understood from the catechism: "We should fear and love God that we may not hurt nor harm our neighbor in his body, but help and befriend him in every bodily need."
Of course, that was not his only sin: he disobeyed the first commandment, making money his god.
Both of these (along with all others) are forgivable sins, sins covered by the mercies and merits of Christ. But the rich man's actions are described to show us that he did not love God, and did not rest on God's riches, but rather on his own.
Notice the contrast in vs. 22: Lazarus dies and is carried to Abraham's bosom. The rich man dies and is buried. This is a picture for us that while the Christian dies, death is a temporary stop. Our ultimate destination is there with the faithful, Abraham being the prominent man of faith.
Note vs. 24: the rich man finally begins to pray! But even his prayers are self-serving. He shows no remorse for his lack of love toward others, Lazarus being the named example. He likewise continues to treat the now exalted Lazarus as one of the hired help: "Abraham, send him!" Instead of begging God's mercy, he dictates to God what and how God shall do His business.
The dictating to God continues. His 5 brothers are -- like us -- to hear God's word, and not expect religious tricks and gimmickry. But the rich man is there to command God as to how and when He should preach His word. The rich man deems God's word insufficient and inadequate, and believes that if a gimmick came along -- a man risen from the dead -- they would believe. Abraham correctly notes that those who will not hear God's word won't believe, even when the gimmicks and tricks come along.