Good question. I would say that God always has the right to take or give life. His will in the given situation is reflective of His never changing, sovereign right over His creation. It's not possible for God to be guilty of murder because He always has the rights over His creation's lives.

To answer what you asked about exegesis I would say that any verses proclaiming His sovereignty are stating this. God always does what He (the perfectly wise, just and holy God) wants. Calvin said that the universe is the "theater of the glory of God" and so God's actions in the universe are the displaying of his nature.

*My point was that God's infinite and immutable nature make accusations of arbitration nonsensical. If God's own nature defines right, wrong, and justice, and is unchanging then assigning a term like "arbitrary" to Him seems blasphemous. Their (Non-christian's) use of the word arbitrary seems to indicate that they see God as a peer who happens to be a bigger and stronger bully not the perfectly wise and holy God.