The rich man's bad deeds outweighed his good, and so he was consigned to one of the less desirable stations. (Specifically, the story explains: the "pivot of the door" to the underworld is "planted in his right eye and rotating on this eye whenever the door is closed or opened." Understandably, his "mouth was open in great lamentation.") In contrast, the poor man, whose good deeds outweighed his bad, got to spend eternity in the company of the "venerable souls," near the seat of Osiris. Plus, he got the rich man's clothes: "raiment of royal linen". (The rich man in Luke's story wore "purple and fine linen".) The moral of the story, "He who is good upon earth they are good to him in Amenti (the underworld), while he that is evil they are evil to him."
Luke's story about the rich man and the poor man seems to have no precedent in earlier Jewish or Christian tradition. So there is indeed a chance that Luke heard or read the Egyptian story and adapted it for Christian use. But we'll probably never know, and anyway, that isn't the point. The point is that, whether or not Luke borrowed this particular story from Egypt's heritage, this theme—immediate reward in the afterlife—must have come from somewhere, and the likely source is one of the religions with which Christianity competed in the Roman Empire.