Euthyphro dilemma

[SteveII]

The first horn "is something good because the gods will it" or
The second horn "do the gods will it because it is good?” but now
The third option (that has no unwanted conclusion): it is not God's will that defines the good but his unchanging nature that governs his will and his commands to us.

With a third option, there is no dilemma. The defeater of the dilemma is to point out that God's goodness is a necessary property (which is a third option). Goodness is not a property that God could have lacked. As the greatest conceivable being, there is no possible world where God is not good.

"Goodness is not a property that God could have lacked."
Whether or not God could have lacked the property says nothing about whether the standard of goodness resides with God, or outside of him.  Those are the only two options, and dressing it up with fancy terms like "necessary property" do nothing to evade the dilemma.

"As the greatest conceivable being, there is no possible world where God is not good."
Again, this doesn't resolve the dilemma.  The question is not, "Is God good?" but rather, "Why is God considered to be good?"  Your objections about necessary properties and such do nothing to resolve that question.  You're still stuck on the horns of the dilemma, you've simply introduced a red herring.  Either the standard of goodness comes from God, in which case it's arbitrary, or it comes from outside him, and he is not the source of morals. There is no third place it can come from.   Moreover, the ontological argument is fatally flawed, so bringing things like "the greatest conceivable being" into the equation only undermines your argument.  Essentially, all you're saying is that God is good because you define him to be so; that isn't any kind of "third option."

Are God's eternal unchanging moral properties arbitrary? Could they have been any other way? Perhaps, perhaps not--I don't think that is clear. I don't think it matters however, because you need God's nature to be arbitrary not in the sense that if could have been different, but that it still can be different. A nature that changes is a defect and not compatible with omniscience so that is not a coherent argument. If it is unchanging, and governs the actions of God consistently, then the dilemma is broken because neither horn applies.