~ Little Pieces of Nothing ~
"That would be murder and I would have to arrest you."
It's an empty threat and they both know it. (Although Katherine probably wouldn't, if she were in any state to perceive what's going on in the room around her. Which is a moot point, but the thought of it crosses Damon's mind all the same.)
Liz could probably actually arrest him if she really tried. She has the skills and the equipment to take down a vampire of Damon's age and strength, and she knows him well enough to be able to get inside his guard and tranquilize him with vervain. It's not like she hasn't done it on several occasions before.
He is reasonably sure that she doesn't actually want to hurt him, even temporarily, unless it's absolutely necessary. She's just trying to stop him from doing something he'll regret, and doesn't know how else to make him listen.
And so he lets her words stop him.
~oOo~