Did God cast Abraham off after he sinned in Egypt?
No. Abraham sinned in Egypt by calling Sarai his sister, but God did not kick him out. As a believer, he had to recognize his sin, and the same grace that restored Peter after his denials applies: confession brings reconciliation, not being cast off.
Les explains that Scripture is full of people who failed miserably, and Abraham is one example. In Egypt, Abraham feared for his life because Sarai was beautiful, so he told her to say she was his sister rather than his wife. That was sin. Yet God did not kick Abraham out. Instead, Abraham had to come to the place of recognizing his sin as a believer. Les connects this to Peter, whom Jesus prayed for so that his faith would not fail. Peter denied Jesus before a servant girl, the cock crowed, and Peter wept bitterly because he was convicted of his sin. But it did not throw Peter out; he was reconciled immediately when he confessed his sin. So it is with a believer in Paul's doctrines of grace. Paul never gives license to sin, and John writes that believers should not sin, but if they sin, confession and restoration remain.