The lies may be part of it, but if you didn't fire them for the COC/SH violation, you would be in for near infinite liability because it ends up as evidence that the culture from the top was tolerant of violations, etc. THis is not conjecture, it's what has basically always happened in the legal realm when companies try to work around it.
In my company, it's explicitly not forbidden, but the relationship has to be disclosed to HR early on (source: yearly training). That being said, I'm not sure what HR is going to do with the information.
[1] https://www.reuters.com/technology/former-nvidia-ceo-huang-h...
Some people get to have affairs with subordinates, others don't. It's a question of if they have the support of the people pulling the levers or not as to whether it's considered acceptable. Universal rules are for little people, once beyond a certain position they are merely tools for selectively shutting out opposition.