From my study notes, kind of rambling on this subject, about 5 years ago. Food for thought:
LFW and Aseity
One can simply point out that God certainly has libertarian freedom in some ways, while He may not have it all ways (like with regards to lying or sinning, since He cannot deny Himself). God was free to create or not create. Otherwise, we would have to view creation as something that God could not avoid doing. That would mean that God had to create, which seems to threaten His aseity. Likewise, if Calvinism is true, this would also mean that God had to elect the ones he elected and reprobate the one's he reprobated. This again would seem to threaten God's aseity. It would also strike against the common Calvinist claim in trying to avoid focusing on reprobation by saying, "God didn't have to elect anybody, so was entirely gracious in electing only some." But if God does not have libertarian free will with regards to election, then he did have to elect some. He was necessitated in some way to do so, couldn't have done otherwise.
If God can only do good (which I believe), then this would seem to create problems for the Calvinists with regards to God's eternal decree, i.e., God causes sin by way of His decree. All that God does is good. Therefore, causing sin is good. Is the Calvinist ready to accept this? Probably not. They will make a distinction between what is good for God and what is good for man. But that distinction could also account for why God can be good and not free to do evil, while we cannot be morally free and not at least "able" to do evil.
So one way to look at it is to see that since God is by nature good, his moral goodness is not tied up in His ability to do evil. Our moral accountability, however, might indeed be contingent on the ability to obey or disobey based on the fact that we are contingent beings who are accountable to God. It may be that as contingent beings, the only way for us to attain moral goodness is through the ability to either obey or disobey God, who is in very nature good. This seems to plainly be the case in Scripture.
It may be that God's moral character was freely chosen by God from eternity. It was an eternal yet free choice on God's part to define His character as He has defined it, which is "good" and is therefore where all standards of goodness find their meaning. This does not mean that there was ever a time that God was not good, and it does not imply that there was ever a moment where a choice was made regarding God's moral character, only that God's moral character is ultimately subordinate to God's will. His choice of moral goodness is as eternal as He is, and is likewise fixed from eternity. Some Arminians are comfortable with this approach and others are not. For those who are not, I think the above is the best alternative (that I can think of anyway).