How can we be held accountable for a lack of belief and immoral lifestyles if God chose not to reveal himself to that person? How can that be fair?
This all depends on what reality is regarding God's actions. From a biblical viewpoint, God is manifesting the divine reality both in the physical universe and in psychological revelation in such things as the human conscience (Read Romans 1:18 through to the end of Romans 2).
This type of evidence for God is reflected in philosophers who support a “natural theology”, the universal evidence of a human conscience in a sense of right and wrong, and now some people speculating there is such a thing as a “God Gene” may point to humanity being “hardwired” in some complicated way to be aware of the divine.
So if God has given a revelation of the divine reality and the reason for a lack of faith is due to an indifference, neglect, or apathy towards such revelation then there would be grounds for a moral failing in people omitting their duty to seek the truth. If we have no obligation to seek truth or accept the truth, then all human knowledge would be lost. Also, people who have more revelation will be held more responsible than people with less.
The Christian concept of God is one in which the Creator is 100% fair in the moral judgment of human beings and takes no pleasure in their failing their moral obligations. But human beings are 100% responsible for their moral behavior (Ezekiel 18).
So while it is true that if God had failed to reveal either the divine existence or moral standards to a person it would be unfair for that person to be judged by things he/she were ignorant.
However, if as the Bible states, God has given adequate information about the divine presence and moral obligations to every person, it is, therefore, fair and just to hold them accountable for their behavior. The reason God can hold people accountable is that they are not without information about God or their moral responsibility.