The confidence and purpose with which Lex moves now that they're headed outside earns him another point of respect from Adrian. Of course he thinks it's a touch on the foolish side to go into a fight with plenty of weapons but no defensive protection, but that's what Adrian is there for.

It's certainly still entirely possible that Adrian is simply insane and the costume is part of a well-funded delusion, but the fighting skills he exhibits once they encounter some of the city's invaders speak to a level of both natural ability and training that suggests just maybe he's telling the truth. He wades into the fray like someone who's done this kind of thing before (although he has to adjust his approach to accommodate the fact that these are definitely not humans he's fighting), always careful to keep an eye on Lex's situation, ready to intervene if necessary. Not because he doesn't think the other man can take care of himself -- it's very obvious Lex knows his way around a weapon or two -- but he isn't the one wearing bullet-resistant full body armor.