Henry Stone simply didn't want such a kind person to die in front of him, so he wanted to speak up for Faye Lockwood, hoping Luna Warner would spare her for the time being.
They had originally captured Faye Lockwood to use as a hostage. If they killed her now, it would only escalate the conflict.
Most importantly, Faye Lockwood had stayed behind to take care of him earlier. He might have been the one to die otherwise, and he couldn't be ungrateful. That was why Henry Stone was determined to keep her alive.
However, his words were completely useless on Luna Warner. She just muttered, "So now you've gone soft on this woman. You can't bring yourself to do it. You want to save her."
