Lex froze, and shifted his gaze from the badge to Liz. He was not overwhelmingly shocked - not shaken to his very core, as Liz would have preferred to see him, but the surprise in his eyes was good enough.
Truthfully, everything Liz had told him before the lake had already proven how valuable the badge was. Even if it wouldn't be immediately useful to him, the badge would inevitably come in handy over the next few years. Even if he could access the Dream realm with the tavern, that would merely lead him to a random location inside the realm.
Whether he could even locate the places that contained those special privileges was in question, let alone whether he could access them. Yes, technically, he did know the big boss behind the scenes. But Lex was never one to hang on coattails and ask for excessive favors.
Only in extreme situations or when someone's life depended on it would he depend on external help like that.
