Lex does some truly stupid things when it comes to hiding his identity. let's wear a Mask that makes you look like a Devil going to a fortress that just suffered a major attack that's occupied by a force who hates Devils
In the end, he decided to get some sleep, and then think more about the matter when he woke up. Besides, he had other things to do - he couldn't spend all his time on this.
is this another example of putting off minor things that have lasting effects
All dressed, he teleported out of his room as himself, and in the garden behind the Midnight Manor. It did not matter to Lex that the emperor was in the vicinity - what did he, Lex, have to do with the fact that the emperor wanted to meet the Innkeeper?