Norman is alive and is in fact doing great. The series is an adaptation of the manga of the same name and as they are following the same story, Norman is alive. He does not die in the manga and with the revelation in season two of the anime, it is clear that we are not done yet with Norman’s character.
Norman reveals that after Isabella had taken him to the front gate, he was instead passed to Lambda rather than be killed like the others. This is a lab where demons drugged and experimented on children in order to mass produce better quality meat.