What we know is that LV was a descendant of the second Peverell son and that Harry is a descendant of the third son. Assuming that the three sons had the same father, this would make Harry and LV descendants of him. Since the eldest son was slain, the second son would continue the line of heir, and therefore LV would be the heir not Harry even though their lines meet. What we don't know is if the sons lived before or after Slytherin. Was Slytherin a descendant of the second son or was an ascendant of the mother of the three sons? Since Slytherin was known to put his mark on everything he could, it may be safe to assume he married a descendant of the second son and took the ring for his own. We have never been told much about the personal life of Slytherin except that he and Gryffindor were the best of friends. This may imply that he also lived in Godrics Hollow. If they were the best of friends, they were about the same age.
My theory: Godric Peverell was the father of the three sons and established the hamlet of Godrics Hollow. Some unknown Slytherin married into the line of the second son , and some unknown Gryffindor married into the line of the third son. Godric Gryffindor being named for his ancestor. Harry is not the heir of Gryffindor, but he may be a descendant. Gryffindor was in control of one of the relics and Slytherin was in control of another. For the time being, the third was lost. Aware of the fact that Slytherin might gain control of the third relic, Godric had the goblins make a sword which could control them. The rest is history.