"When the men of that place asked him about his wife, he said, 'She is my sister,' because he was afraid to say, 'She is my wife.' He thought, 'The men of this place might kill me on account of Rebekah, because she is beautiful.'" NIV translation
Here, we see that Isaac did not trust God to protect him and Rebekah and so he fell into the same sin that his father had committed (Genesis 12). Abraham had told a half-truth while, with Isaac, it is a total lie.
"When Isaac had been there a long time, Abimelek king of the Philistines looked down from a window and saw Isaac caressing his wife Rebekah. So Abimelek summoned Isaac and said, 'She is really your wife! Why did you say, "She is my sister"?' Isaac answered him, 'Because I thought I might lose my life on account of her.'" NIV translation
The king saw Isaac and Rebekah together and knew they were married. He immediately asked Isaac why he had lied.
This is a reminder to us that, as God's children, even the world expects us to be different. We also need to remember that fear of anything but God is not of God. Isaac's fear arose from his lack of faith (trust) in God.
"So Abimelek gave orders to all the people: 'Anyone who harms this man or his wife shall surely be put to death.'" NIV translation
We must remember that Abimelek was a pagan and yet he ordered the protection of Isaac and Rebekah. This can only be the favor of God and it is interesting to note that this favor is granted even while Isaac had lied (sinned).
"Isaac planted crops in that land and the same year reaped a hundredfold, because the Lord blessed him. The man became rich, and his wealth continued to grow until he became very wealthy." NIV translation
Isaac was successful in all that he did and he became very rich. He would have already had more than most men as he received his inheritance from Abraham who was very wealthy. Why would God bless a liar? Even though he had sinned, Isaac was still God's chosen servant and his blessing would have been a witness to the Philistines.