All's fair in love and war
Typically, Lex had a lot of confidence in himself. He had proven his competence at every turn, and achieved much in his short life. But he knew when to admit that he'd met someone better than him, and that is exactly what happened.
Lilith had melted like butter in his hands, and she was practically inseparable from him. He didn't want to pry into their private matters so he didn't check her age, but he was certain she wasn't exactly a teenager, so it was quite admirable how easily she had swooned.
Of course, Lex also used his own sixth sense to judge if she was doing this just to get close to him. The devils did not have a stellar reputation to begin with, and it wouldn't even be the first time they targeted the Inn.