"In season 4, another scene came up where Kate was undressing and I fought very hard to have that scene be under my control.
"And I failed to control it again. So I then said, 'That's it, no more. You can write whatever you want — I won't do it. I will never take my clothes off on this show again.' And I didn't."
Lilly said her character was "kinda cool" but as the show went on "she became more and more predictable and obnoxious."
"I felt like my character went from being anonymous, really having her own story and her own journey and her own agendas, to chasing to men around the island. And that irritated the s**t out of me," Lilly said.
"I did throw scripts across rooms when I'd read them because I would get very frustrated by the diminishing amount of autonomy that she had and the diminishing amount of her own story that there was to play. There's nothing wrong with women's lives being characterised by their relationships.
"I think that often happens to men and women. But there was this eventual lack of dimension to what was going on with her," she said.
Lilly is currently promoting her new movie Ant-Man and the Wasp, in which she plays the first female Marvel superhero to headline her own film.