Was it a show of lack of faith in Abram in Gen 12:12?
Genesis 12:7 The LORD appeared to Abram and said, "To your offspring,
I will give this land." So he built an altar there to the LORD, who
had appeared to him.
Why did Abraham make such an unusual request: that Sarah presents herself as his sister in Egypt?
Genesis 12:10-13 NASB
10 Now there was a famine in the land; so Abram went down to Egypt to
sojourn there, for the famine, was severe in the land. 11 It came about
when he came near to Egypt, that he said to Sarai his wife, “See now,
I know that you are a beautiful woman; 12 and when the Egyptians see
you, they will say, ‘This is his wife’; and they will kill me, but
they will let you live. 13 Please say that you are my sister so that
it may go well with me because of you, and that I may live on account
Sarah, if view as a married woman, an Egyptian could only get her by murdering her husband or her owner, but if viewed as a sister there was the likelihood that she could be bought from her brother by amicable means.
Abraham's fears were not groundless, soon after arriving in Egypt, the Egyptians simply took Sarah to Pharaoh's house, without asking or negotiating for her.
Genesis 12:14-16 NASB
14 It came about when Abram came into Egypt, the Egyptians saw that
the woman was very beautiful. 15 Pharaoh’s officials saw her and
praised her to Pharaoh, and the woman was taken into Pharaoh’s
house.16 Therefore he treated Abram well for her sake, and gave him
sheep and oxen and donkeys and male and female servants and female
donkeys and camels.
Following this, God intervened to protect Sarah and struck Pharaoh's house with severe diseases:
Genesis 12:17 NASB
17 But the Lord struck Pharaoh and his house with great plagues
because of Sarai, Abram’s wife.
When the truth was revealed to Pharaoh, he said to Abraham. (The scriptures do not tell us how this was revealed to Pharaoh)
18 Then Pharaoh called Abram and said, “What is this you have done to
me? Why did you not tell me that she was your wife? 19 Why did you
say, ‘She is my sister,’ so that I took her for my wife? Now then,
[h]here is your wife, take her and go.” 20 Pharaoh commanded his men
concerning him; and they [i]escorted him away, with his wife and all
that belonged to him.
Some have criticized Abraham as a liar and a coward, we should not rush to judge him, since we do not know the circumstances nor the conditions that prevailed in those days. We will hear his side of the story when the resurrection takes place, John 5:28-29. History has shown that Abraham's fears were not unfounded, about ten years later a similar event happen with the Philistine king of the city of Gerar, Abimelech Gen. 20:1-7, again God intervene to protect Sarah. Many years later, Isaac, like his father Abraham, used the same strategy by claiming his wife Rebekah was his sister. Gen. 26: 7-33. Again God intervened to protect his servants and the line of the seed.
Abraham, therefore, acted in harmony with what he felt would be the safest course in having his wife identify herself as his sister. She was, in fact, his half-sister. Genesis 20:12.