Your premise is flawed, Bonaparte. Sarai was Abraham’s sister. They shared a parent.
Yes, she was his half-sister (Gen 20:12) and also his wife, according the Bible --
As for Smith's claim in Pearl of Great Price that God told Abraham to lie to Abimelech, it is found nowhere in the Bible.
In the Biblical account, neither God nor Abraham lied. Abraham let Abimelech make his own assumption and God took care of the rest, appearing before Abimelech in a dream and (again) letting Abimelech make his own assumption.
Both my premise and my conclusion are true.