"Is the parable of the rich man and Lazarus a true story" is, I believe, the wrong question to ask. It would be like asking isif the story of the Good Samaritan is a true story (for the record, I don't know). The point is that the Good Samaritan is an instructive story set in reality. The story would be much less impactful to a Jewish audience if it didn't involve a Samaritan between Jerusalem & Jericho.
I suggest that the phrase "under the sun" should be read as a description of the activities/affairs/interests of this life - this is the focus of Ecclesiastes 9 - death brings about the end of the vanities of this world.