Abraham came to live among people he knew nothing about. Abraham served God, but if the people of this region knew God, he did not know. God had revealed Himself to Abraham in Harran - a land where people did not serve the Lord - and He had sent him to Canaan (Genesis 12:1). Despite this revelation of God, Abraham did not feel superior to other people, he even did not rule out the possibility that the people of Canaan might know God too. Yet, he was not convinced of this, and therefore he considered the possibility that they might kill him because of his beautiful wife Sarah.
Often we think God was only the God of the Israelites, but here we see clearly that God not only revealed Himself to Abraham, but that others too knew the Lord. God came to Abimelek in a dream one night, and Abimelek knew the Lord so well, that he could not believe God would destroy an innocent nation. Abimelek feared the Lord, and he could testify that he was innocent, that he had a clear conscience and clean hands. And that is the reason why God had kept him from sinning.
No, God is not only the God of Abraham, He is the God of everyone who listens to Him, like Abimelek. And when God has mercy on us, we may know that He keeps us safe and holds us, so that the evil one cannot harm us. But if we want to be safe in the hands of the Lord, then we must not despise His word, but obey His command: listen to the prophet, ‘and he will pray for you and you will live.’