Allright, we have two options. We can lynch (most likely at random), or we can no lynch. While you would think no lynch is the better option in this scenario, it is not. If we lynch, the mortician will be able to see what happened. If we don't lynch, the executioner is going to kill someone* and we will never find out anything about whoever he kills.
*look at the player list, as meta as this sounds, I think most people on there actually would kill someone at random with this role.
Of course this brings me to the third option, which is hoping that the executioner reads this and doesn't execute anyone should we decide on a no lynch, which we can also try.