I thought there was a dress code, as in proper attire (although don't know that proper attire is defined). But I can't think of anyone who would consider a bathrobe in a public area (short of a pool & on the way to/from it) 'proper attire', and an executive lounge is a public area. It's certainly not someone's bedroom/bathroom.
At Grosvenor House in London there was a I think I'm cool & I'll do what I want American who came in & strutted around in a bathrobe. It wasn't a pretty sight, and everyone in biz attire just stared at the man increduously. The lounge attendant tried to explain to him that his bathrobe wasn't proper attire. He argued with her saying that he liked to be comfortable. At that point I did say something to him to help back-up the lounge attendant - and also suggested to her that if he continued to not comply, she consider calling security. He decamped to his room right after that.
In Vienna a couple of weeks ago I was at the Hilton Stadtpark & a guy came in with bathrobe on. Again, everyone stared like are you nuts. The attendant was very pro-active. As soon as she saw him, she went over & politely but firmly told him that he was not allowed to be in the lounge in a bathrobe. He changed & was back 3 minutes later in polo shirt & jeans.
Cheers.