"Please say that you are my sister, so they will be good to me for your sake, and my soul will live on account of you." (Gen. 12:13)

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 was anything less than Sarah's brother the Egyptians would not have any interest in securing his goodwill.

When Abraham added that, "my 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: "so that I will survive." The words "my soul will live" is an allusion to Sarah's remaining spiritually uncontaminated. We have a tradition 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. (Proverbs 13:25) Abraham was motivated by similar considerations.

...he hoped he would experience physical wellbeing as well as spiritual wellbeing...

The reason Abraham appears to repeat himself when he said: 1) for your sake, and: 2) because of you, is that he hoped he would experience physical wellbeing as well as spiritual wellbeing due to Sarah's describing herself as his sister.

Our Sages (Berachot 31) explain "If see You shall surely see.." (I Samuel 1:11) to mean that if G‑d would see Chana (i.e. pay attention to her prayer) and would grant her a child, all well and good; if not she would place herself in a compromising situation where she would surely be seen, which would force her husband to treat her as a sota, a woman suspected of marital infidelity. Once she would drink the waters prescribed for such a woman (Num. 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 sota finds herself in, he and she would have a child thus assuring Abraham of his future, "my soul will live on."

The letter vav in vechayta ('will live') 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 "will be good to me", 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 Abimelech, 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. (Gen. 20:15)

It is even possible that the fact that Sarah twice found herself in the position of a sota, a woman unjustly suspected of marital infidelity, once in the palace of Pharaoh, and then again in the palace of Abimelech, 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: "if the woman has not become defiled and has remained pure" (Numbers 5:28) this refers to her neither having been unfaithful with the man with whom she is now suspected to have been unfaithful, nor with any other man. In such a case she will be unharmed by the waters she had 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 sota. The expression "my soul will live" would refer to Abraham having children due to the chaste conduct of Sarah.

[Selected with permission from the five-volume English edition of "Ohr HaChaim: the Torah Commentary of Rabbi Chaim Ben Attar" by Eliyahu Munk.]