Lu Yurong's plan was obviously to have Chu Li start a conflict with the Secret Guardians Hall, battling each other to the death. Then, she could take the opportunity to weaken Gu Yu's current position, forcing him out of that spot.
However, this would cause also harm to Chu Li in the process. With that in mind, she was prepared to mock him for it.
Initially, Chu Li did not want to be the first to make a move, he wanted to be the one who tramples on Gu Yu's pride. Gu Yu was getting more and more extreme. After the last time, he became even worse and crazy.
Now that the situation had changed, he had better things to do. Hence, he changed his mind and took the opportunity to leave King An's Imperial Palace, making it look like he was surrendering to the Secret Guardian Hall.