Or HaChaim on Genesis 12:13/אור החיים על בראשית י״ב:י״ג

1 למען ייטב לי בעבורך. In order that I will receive benefit on your account. Abraham explained why he asked Sarah to describe him as her brother and not as some more distant relative or a total stranger. If Abraham's status were anything less than Sarah's brother the Egyptians would not have any interest in securing his goodwill. Abraham may have had yet another motivation for insisting that Sarah describe their relationship to each other instead of he himself. His own words would not convince the Egyptians as they might construe them as a stratagem to be wooed with gifts. The plain reason is no doubt that he was afraid that if he were to say he was her brother and she would say nothing, sooner or later Sarah might make a comment which would reveal that there was a husband-wife relationship between her and Abraham. When Abraham added that וחיתה נפשי, that his soul would remain alive due to the stratagem of Sarah describing him as her brother, he did not have in mind his mere physical survival. If that had been his intention he would have said ואחיה, "so that I will survive." The word וחיתה נפשי is an allusion to Sarah's remaining spiritually uncontaminated. We have a tradition (Proverbs 13,25) that צדיק אוכל לשובע נפשו, that the reason a righteous person consumes physical food is not to indulge his senses but to satisfy the needs of his soul to carry on his task in life. Abraham was motivated by similar considerations.

2The reason Abraham appears to repeat himself when he said 1) בעבורך, and 2) בגללך, is that he hoped he would exprience physical wellbeing as well as spiritual wellbeing due to Sarah's describing herself as his sister. Our sages (Berachot 31) explain Samuel I 1,11 אם ראה תראה בעני אמתך, to mean that if ראה, G'd would see Channah (pay attention to her prayer) and would grant her a child, all well and good; if not תראה, she would place herself in a compromising situation which would force her husband to treat her as a סוטה, a woman suspected of marital infidelity. Once she would drink the waters prescribed for such a woman (Numbers 5,24) her innocence would be established and G'd would have to grant her a child as per verse 28 in that chapter. Abraham hoped that as a result of Sarah's chastity under circumstances resembling the compromising situation a סוטה finds herself in, he and she would have a child thus assuring Abraham of his future, וחיתה נפשי, "my soul will live on." There are numerous instances where our sages have explained the word בגלל as having metaphysical significance, such as in Deuteronomy 15,10 where G'd promises that blessings will devolve upon people already if they merely promise to do charity, דבר (Tossephta Peah 4). The letter ו in וחיתה also has a special significance. Abraham did not mean that the fact that his soul would remain alive would be part of the benefit he would experience through Sarah's lie. Whereas the survival of his body would be an extension of ייטב לי, the direct benefit he would derive from Sarah's lie, the spiritual dimension, i.e. the survival of his soul would be an independent benefit, something that he would achieve later on when Sarah would be alone in the palace of Avimelech, the king of the Philistines. On that occasion he did not face expulsion from the land of the Philistines on account of having been found out as a liar (20,15). It is even possible that the fact that Sarah twice found herself in the position of a סוטה, a woman unjustly suspected of marital infidelity, once in the palace of Pharaoh, and then again in the palace of Avimelech, resulted in her ability to conceive and bear a child. Rabbi Yitzchok, (a teacher of Rashi?) suggests that when the Torah appears to repeat itself in Numbers 5,28, i.e. "if the woman has not become defiled and has remained pure," this refers to her neither having been unfaithful with the man with whom she is suspected to have been unfaithful now, nor with any other man. In such a case she will be unharmed by the waters she has drunk and able to retain seed. Accordingly, Sarah became pregnant and bore Isaac to prove that she had been faithful to her husband each time she found herself in the situation of a סוטה. The expression חיתה נפשי would refer to Abraham having children due to the chaste conduct of Sarah.