Casual
Normally, Lex could have teleported directly to Moon. But since he wanted to show Liz the place, he teleported a little far away. Also, temporarily, he disabled Liz's permission to leave the Inn.
After he showed her Moon, told her the situation and handed her a golden key, he would once again grant her exit rights. It was not like he could actually kidnap her. He just thought showing her everything would be a lot quicker than explaining it to her. Not to mention, she was clearly very defensive because she felt like Lex had ulterior motives.
Their arrival inside the Inn clearly stopped her attacks on him, which was good. As he exited the building, he arrived in a nice little society, filled with unusual looking houses and countless people in suits.