The place taken were in the building, where their memories made. Lucian was surprised that his name was just a past and he was supposed to be called a new name. Due to his condition, he can't remember it and it hurts him. That's why he's angry in that convo. Lyon was there too and surprised that Lucian was also an experiment object with different affection. The friend Lyon mentioned was a "real" friend. He used to have a friend with different name. Their personality were the same as Lucian's. Because of that, Lyon has experience with become friends so he wants to become a friend for Lucian. He knows his past friend's name but he doesn't want Lucian have that name so he uses Lucian's name.