With regard to the "It was a clue Lorca was from the Mirror Universe!" hand-wave, it doesn't work, because season two mentioned that Tilly went to a grade school named after Musk. You could alway double-hand-wave and say her school was named after a different Musk (or even the concept of "musk," maybe it was in a smelly part of town), but I think it's more honest to just say they whiffed it. Not the first time in Trek, and won't be the last.