Is what is morally good commanded by God because it is morally good, or is it morally good because it is commanded by God?
If the former, then there is something (morality) greater than God, that even God must conform to. If the latter, then God is arbitrary and not reasonable at all.The answer requires the acceptance of only two concepts. If, for purposes of argument, we accept two propositions: (1) each being has its own characteristic nature, and (2) God is pure existence, the source of all existence, then there is no dilemma, at least none in Christian theology.
Morality is not the result of God issuing commands.
The moral life is who God is and God does not change.
Now, one may respond that anything which does not change is dead, yet that response cannot explain the fact that, even on the physical plane, we are composed of things that do not change, yet we live.
God is pure Act, pure Being. Morality is the nature of God. To say that we conform ourselves to moral law is to say we are only fully ourselves when we live as the image and likeness of the God in Whose image and likeness we are made.
Socrates' false dilemma comes from the wrong idea that morality is a command.
Morality is Being. Morality is Act. God is pure Act. When God reveals Himself to us, even through the physical revelation that is the physical universe (the heavens are telling the glory of God), our being responds to His self-revelation. Even physical contact with the universe elicits a response from us (we, who are made in His image). We respond with an answering recognition, a desire to live as He lives, to "be ye holy as God is holy." This is the moral compulsion each man experiences. It is not a command from God, it is our own human nature responding to His divine nature - Deep calls to deep across the void. God does not command us to live according to His moral law. Rather, if it can be considered a command at all, we command ourselves to live the moral law, because - when we encounter Him, even if ever so remotely - we innately and inchoately desire to live as He lives.
Socrates and every other philosopher who saw the relationship between God and "His commands" as a dilemma only saw it as such because they didn't understand what Augustine, Anselm, and Aquinas did understand. Morality ultimately isn't about command. It is about image and likeness, Persons and personhood, God's Own Divine Nature and its (broken) mirror, our human nature.
Socrates could not understand this because he did not have the tools. The idea of "person" is a Christian idea. The word "person" was stolen by Christians from Greek stage plays and redefined to help people understand the three Persons of the Trinity. Since Socrates did not have the Christian understanding of either "person" or "nature", he could not resolve the problem that he faced. He believed in God, but - without the revelation of Jesus Christ - he didn't know how to answer the dilemma he faced.