I don't remember Desmond having a lover throughout the series. He didn't have one before so how would he have a son? The only person he might've gone with to have a son with would've been Lucy but since she was a Templar and died he couldn't of. He also never had any relations with Rebecca, so that can't really be. So therefore, Desmond would still have to be alive. My guess is Minerva takes his soul or whatever then scolds him, then revives him to wake up suspiciously next to the animus.