What does Genesis 20:11 mean?

Abimelech has asked Abraham a reasonable question. He wants to know why Abraham lied about Sarah being his sister. This resulted in Abimelech taking Sarah as a wife, and nearly committing adultery as a result (Genesis 20:2–5). Why did Abraham do this thing and bring the wrath of God on Abimelech and his innocent household? Abimelech is pressing the question very directly: he wants to understand what would lead Abraham to do such a thing.

Abraham's answer reveals how his fear in that situation overcame his faith in God, and an apparent misunderstanding about the faith of Abimelech and his people. Abraham believed there was no fear of God in Gerar. He believed someone might kill him to take Sarah for his own. Notice that Abraham, again, was not wrong about Sarah's desirability. She must have been extremely attractive. Both in Egypt years earlier and now in Gerar, the most powerful man in the area quickly took her for his own wife (Genesis 12:14–15).

Abraham was wrong, though, about God's ability and/or willingness to protect him and Sarah. His lack of faith is hard for us, as readers of the Bible, to fully understand. Abraham has literally walked and talked with the Lord. He has seen God utterly destroy the wicked people of Sodom and Gomorrah while rescuing his own nephew Lot from among them. He has received blessing after blessing from the Lord, alongside powerful promises, including one that Sarah will bear him a son within the year.

Abraham was also wrong, it seems, about the lack of faith in God in Gerar. If they didn't have it before, the king and his people certainly learned to fear the Lord very quickly under threat of death from God.