If he didn't break any laws, why is he in the predicament he finds himself?
By refusing aid to Lazarus, the poor man, the rich man broke both the first and second commandment. 'Upon these two commandments hang the whole of the Law and the Prophets.' Matthew 22:40
'Love does no wrong to a neighbor; therefore love is the fulfillment of the law.' Romans 13:10
'And the King will answer them, ‘Truly, I say to you, as you did it to one of the least of these my brothers, you did it to me.' Matthew 25:40
Consonant with these teachings, giving practical help to the afflicted is the sole criterion which God, himself, has given in the whole of Scripture, on the basis of which we will be judged.
'If anyone says, "I love God," and hates his brother, he is a liar; for he who does not love his brother whom he has seen cannot love God whom he has not seen.' 1 John 4:20
As Pope Francis has mentioned, it's not primarily about a rule-book, the letter of the Law, but about an encounter - with the person of Christ, through the Holy Spirit. Just as the Jewish people of old were incapable of keeping the Law perfectly, neither are we.
Though, if we live our lives in a spirit of charity, of generous, disinterested self-giving to our fellows, we shall become increasingly observant, whether consciously or not, of either the formal teachings of Christ in Scripture and the Church, or of such demands upon us as Christ makes informally through the Holy Spirit - and in which the most self-righteously punctilious in their observance will have no say at all.
This parable is ultimately based on the cardinal truth, that it is upon the disposition of our heart, not on rules and regulations that we shall be judged:
'Where your treasure is, there your heart will your heart be also.' Matthew 6:21
As a general rule, the rich do not come out of the Bible with a good image; indeed, they are constantly held up, notably, by the Psalmist and the prophets, as figures of wickedness; the poor as the true Israel, the virtuous man. And I'm afraid, pace our new Pope Francis, the Virgin Mary's Magnificat sounds awfully like a fire-brand's version of an ideology of poverty.
'Go and learn what this means, ‘I desire mercy, and not sacrifice.’ For I came not to call the righteous, but sinners.”' Matthew 9:13
I've always had the impression that Jesus was laying on the sarcasm rather heavily in the last sentence, above.