This is an ancient dilemma.
Socrates asked Euthyphro, "Is the pious loved by the gods because it is pious, or is it pious because it is loved by the gods?" Socrates was asking if morality must come from the gods to be good, or is it good anyway and therefore loved by the gods.
Many theists argue that morality is separate from God, that God only loves morality because it is good - Thomas Aquinas for instance, holds that humans through reason (from God) can seek out what is moral to what is immoral. It is 'reason' that is a gift of God, not that morality itself stems from God.
Morality only stems from God in a theistic argument if they believe in a Divine Command Theory of morals, ie what is moral is only moral because it comes from God - this is, however, a minority opinion among theists - and incidentally, not necessarily the view of JW's. Not least, because this means there is no measure on morality, other than God's will. Many others argue that God commands what is moral, because it is moral - ie God and morality are separate.
Romans 2:14,15 even tells us that the Gentiles have the law written on their hearts, that it is through their conscience that they do what is right.
If God and morality are indeed separate, then we can be moral without any belief in God or god.