Honestly I wouldn't say life is fair but more like it tries to balance things out.
As per your example: People who are born into rich families are often not very united as a family because they focus mostly on work, their businesses and trying to maintain their wealth as oppose to poor-to-average families who have a lot of chance to connect with each other due to them living in an average-sized house.
People who are beautiful/handsome might look like they have it easy, but the most common problem they face is finding a true and real partner. It is no hidden fact that people are attracted to beauty and that is why for this people they really need to test first if it's not only the physical appearance or lust the other party wants and feels about them.
Not really sure if this is a good example of people who have great luck but for simplicity's sake, people who have won the lottery. True they are somewhat blessed at one point in their life but if they don't know how to manage the money nor know who to trust, then their winnings could be gone in less than 5 years.
So in a way, nature tries to balance things out.