If you think that mat was not lucky before going through the doorway, read the books again. Read the account where he is in Tar Valon. He's constantly winning at dice. He even remembers being lucky, jut never this lucky. And that is all before going through either doorway. the luck has nothing to do with those. He is not a hero reborn. Most of the heroes that keep getting reborn are tied to the horn, and they all came when he blew the horn. Does anyone want to argue that he could exist as two people at once? The memories came from going through the second doorway. Get a clue. In LoC even he thinks that sometimes they seem to be random.