Lloyd Slate outright lied when he said that he didn't kill the Summer Knight.
Harry - Did you kill Ronald Reuel?"
Slate burst out laughing. "Christ, Dresden. You don't waste time, do you?"
"I've filled my insincere courtesy quota for the day," I said. "Did you kill him?"
Slate shrugged and said, "No. To be honest with you, I'm not sure I could have killed him."
The Winter Knight's mantel doesn't stop him from lying. I don't believe Mab can change this rule because it would interfere with the free will of her Knight. Even if I'm wrong about this, it would diminish her Knight by constraining him in a way that is antithetical to having a mortal champion in the first place. It would be the first step on a slippery downward slope of having a mediocre and ineffective Knight.