She is free to fuck whomever.
She is not free to attempt to have him executed by lying in court. That is a crime, both in westeros, and in our world. I my view lying to get someone executed, or lying in court about someone being a murderer/kinslayer/regislayer is a very severe crime, just as bad as commiting the act itself.
As I read the chapter that was the reason for Tyrion killing her.
Under Westerosi standard, which have been applied to Daenaries and Ned, Tyrion is entitled to revenge/justice, and he has no other way of getting justice.