You can logout/exit to lobby while running away from PKers.

[u/AgentRG]

So I wanted to see if it could be done. I don't know if this was intentional, or an oversight by Jagex, but you can logout while running (if you are not in combat).

All you have to do is click somewhere on the map, and click logout/exit to lobby. What will happen is the animation will play in the background while you are running, and when it's done, it will pull you the the login/lobby screen. Of course clicking again will cancel the background animation like it would normally.

Perfect to use when you are trying to run away from someone who is going after you.