Milena and Arthur wore the cloak since that was needed. On the other hand, Lucifer simply placed the badge on his chest just for the sake of it.
After they were done with the identification, Lucifer took them back to the left, which went to the tenth floor.
"This will be your personal floor. As a head, you're entitled to one. This one was being used by Zhu until recently, but he is gone. It'll be yours. It has everything you may need. Moreover, if you need to contact one of us, there is a phone inside."
"And if you need any more help, you can just ring the bell, and some men will be here to help."
"And lastly, your people can also stay in this place with you. There should be enough rooms. However, if you want complete privacy, they have also been assigned suites on the third floor. You can tell them to leave. They should be able to use the lift."
"That will be all. I'll take my leave now."