The question is about the angel of the Lord. God calls him the angel of the Lord. That means he’s the angel of the Lord.
Except Abraham bargained with Him for Sodom.
There is no question that sometimes God sent an angel to visit with humans. Sometimes, He appeared to them Himself, and called Himself the Angel of the Lord. I believe if you review the episode of the Angel of the LORD in Gen. 22, you will find this to be one of those situations. Notice:
"11 But the angel of the LORD called to him from heaven and said, "Abraham, Abraham!" And he said, "Here I am." 12 He said, "Do not stretch out your hand against the lad, and do nothing to him; for now I know that you fear God, since you have not withheld your son, your only son, from Me." 13 Then Abraham raised his eyes and looked, and behold, behind him a ram caught in the thicket by his horns; and Abraham went and took the ram and offered him up for a burnt offering in the place of his son. 14 Abraham called the name of that place The LORD Will Provide, as it is said to this day, "In the mount of the LORD it will be provided." 15 Then the angel of the LORD called to Abraham a second time from heaven, 16 and said, "By Myself I have sworn, declares the LORD, because you have done this thing and have not withheld your son, your only son, 17 indeed I will greatly bless you, and I will greatly multiply your seed as the stars of the heavens and as the sand which is on the seashore ; and your seed shall possess the gate of their enemies. 18 "In your seed all the nations of the earth shall be blessed, because you have obeyed My voice.""