It's interesting that you should be asked to point out similarities between these parables, because they are about different topics. Perhaps the most significant similarity I can find is that all of them seem (at least partially) intended to correct fallacious assumptions about God in the popular religion of the day.

This religion pictured God as a rather superficial, judgemental figure. It was the same picture many hold today - if you do the right things, God will love you, but if you don't, he'll hate you. It was a bland, man-made "follow this list of rules" religion. The same religion also imagined that God's favor translated into wealth and success in the world. Thus, the society was one in which the poor, the sick, and the less reputable were social outcasts, while the rich, the religious, and those with the outward signs of success were favored. It was into this culture that Jesus crashed like a meteorite.

Jesus tells the parables of the lost sheep and lost son in response to a criticism from the religious leaders - "he associates with 'sinners.'" These parables zero in on God's compassion and fierce, relentless love, particularly to those the world has rejected. He never stops searching for and calling to those he loves, and is always willing to receive any that return, no matter how far they've been. God does not value people according to their outward shows of virtue, as men do - he looks at the heart.

In the same way, God does not value our ability to accumulate wealth, as is pointed out by the story of the rich man and Lazarus. Note that this story closely follows Jesus' response to the Pharisees, who were again scoffing at Jesus because of their love for money. Note his response: "You are the ones who justify yourselves in the eyes of men, but God knows your hearts. What is highly valued among men is detestable in God's sight."

This story, interestingly enough, is not even identified as a parable. Most simply assume that it is, even though it doesn't bear the characteristics of Jesus' other parables - note that the characters in this story are named. Regardless, it tells the story of a man who willfully and persistently rejects God - this is not a man who simply disbelieves at first sight. He had many opportunities to take a path that would lead him to a relationship with God. It's important to note his motivation for doing so - not reason, but self-interest.

This story points out an interesting truth - that most people who reject God on supposedly rationalistic grounds have a deeper reason to for doing so. They simply don't want to have to answer to any god higher than themselves. They fear that doing so would cost them powers and pleasures in the world - whether wealth (as in this and other cases) or simply habits and ways of life they cherish. In this rather common state, people realistically can't be convinced to believe - they have too much invested in their current worldview.