>>50692687Clearly it's this.
Dawn and Lucas never time travel into the past, the protagonist from LA isn't the same person (they have shirts suggesting they came from Galar or Kalos). And since there's no indication that they got to go home after completing the game, the most logical assumption is that they simply remained in Hisui, had families (either with Akari/Rei or seperately, doesn't matter) and then however many years later, Lucas and Dawn exist as the ancestors of Rei/Male Protag and Akari/Female Protag respectively.
Your character doesn't look like Lucas/Dawn because they are Lucas/Dawn, they look like Lucas or Dawn because you become their ancestor after being stuck in the past, which might also be why you don't get to return to the present at the end of the game (because you need to be there so that your eventual ancestors will stop Cyrus in the future).