The parable of the rich man and Lazarus contains many hidden messages. This is to be expected precisely because it is a parable. The only "sin" of the "'rich man" appears to be that he was indeed rich; this might have reflected the deeper sins of selfcenteredness or a certain lack of compassion; perhaps he actively as well as passively abused Lazarus, the poor man.
Jesus' point was to show that if we are too concerned with wealth, we will suffer in the afterlife. We will accrue negative and difficult karma. And let's realistically remember that, to be "rich" in the poor land of first-century Palestine was not the same as being "rich" in twenty-first century America. A "rich" man, in those days, and in that culture, owned his own tiny house and his own donkey, and little else!
Let us, then, exercise generosity at every opportunity so that we do not suffer the travails of "hell states" after this life.