Verses 10-20 tell of Abram's sad mistake.
The famine was a test for Abram who was learning to walk by faith. He had not been brought from Ur in order to die of hunger.
The severe famine should have driven Abram to greater trust. Instead it exposed weakness. Whether it was right to go to Egypt is not the question. It was his wavering trust in the Lord's ability to protect him and his, that led to downfall. It was Sarai's beauty and attraction that were the source of Abram's fears (verse 11-13). His fear of man led to his resolve to save his own life by exposing his wife to danger (verse 13). What he asked her to say was the truth but not the whole truth, so it was a lie. Going "down" to Egypt proved to be more than geographical in this case. What he feared came upon him (verses 14-16). What a warning to us to act in faith, not fear. "BUT THE LORD PLAGUED PHARAOH"
God intervened to protect Sarai and save from the consequences of Abram's mistake. The Lord's plague was kinder than Abram's deceit. It was intended to keep Pharaoh from sinning against the purposes of God irrevocably. Further, the Lord showed that acting in faith is right - because He is able to protect and deliver.
He left Egypt, humbled - but with the new revelation of the Lord's ability to extricate him from all difficulties - even those of his own sinful making.
Chapter 13:1-4 records his return to Bethel. Abram never left Canaan again - one excursion into Egypt was enough. He came out materially, and more important spiritually, richer. When mistakes have been made, go back to Bethel, the house of God.
Genesis 13:5-13 tells of the separation of Abram and Lot, and the fatal choice of Lot.
What sad reading (Genesis 13:7 ). Contention in the household of faith makes an unfortunate impression on those outside, watching. "The Canaanites and Perizites then dwelt in the land." (Genesis 13:7 ). Any inconsistency spoils the witness.
This question (Genesis 13:9 ) brings out Abram's generosity and nobility of character. He gave Lot first choice. He has learned to trust in the overruling guidance of the Lord.
It has been said 'Lot's eyes were the binoculars of his heart.' Looking at the well watered plain going down towards Sodom and Gomorrah, he made his fatal choice (Genesis 13:10-11 ), he pitched his tent towards Sodom. His choices came out of his heart and were made before his herdsmen commenced to drive the cattle to the well watered plain. The full consequences he was to reap later.
After Lot departed (Genesis 13:14 ), the Lord talked with His friend (James 2:23 ), reassuring and comforting him with a more extended promise. Abram lifted up his eyes at the Lord's command. Lot had done so with lust. North, south, east, west, all the land given to his seed forever. (Genesis 13:15 ). Promise different to Chapter 12 in that the land is given personally to Abram and his SEED, and that it is forever. Abram is to possess the land by faith. He is told to
The title to the land was his - it was his right. But as he walked the land it was his by faith. So with all the Lord's promises - where we plant our feet in possession the promise becomes ours. The possession of the land 'forever' is understandable from the interpretation of SEED, being Christ Jesus.
The mighty 'wills' spoken by the archangel Gabriel concerning the holy child Jesus included these:
(See Luke 1:30-33 ).
After being comforted in his faith continued to move and walk by faith (Genesis 13:18 ). Pitching his tent by the trees (possibly oaks) of Mamre (meaning vigour) in Hebron (meaning seat of association) parting from Lot in obedience, he moves into greater faith through imparted vigour, through vision and fellowship with the Lord. He built an altar there.
4.5. ABRAM CONFRONTED STRIFE IN FAITH (Genesis 13:4-13)
4.5.1. THERE WAS STRIFE
4.5.2. "IS NOT THE WHOLE LAND BEFORE YOU?"
4.5.3. "LOT LIFTED UP HIS EYES"
4.6. ABRAM COMFORTED IN HIS FAITH (Genesis 13:14-18)
4.6.1. "THE LORD SAID TO ABRAM"
Genesis 13:17
"Arise, walk in the land through its length and its width, for I give it to you".
Galatians 3:16
"Now to Abraham and his Seed were the promises made. He does not say, 'And to seeds,'
as of many, but as of one, 'And to your Seed,' who is Christ."

He WILL be great 
The Lord God WILL give Him the throne of His father David 
He WILL reign over the house of Jacob forever 
Of His kingdom there WILL be no end
Galatians 3:29
"And if you are Christ's, then you are Abraham's seed, and heirs according to the
promise."
4.6.2. "ABRAM MOVED ... AND DWELT BY ... MAMRE ... IN HEBRON"