Again, unwittingly you demonstrate that the blood came between the inhabitants of the house and the death angel and prevented the death sentence from visiting the house covered by blood.
Intercede: come between on behalf of.
It is intercessory, and it's not to be argued. It's simply a fact.
The lamb WAS sacrificed for the life of the inhabitants of that house. This is so clear. I wonder that you even discuss it.
Exactly. The lamb had to be killed in order for the blood to be used as a covering for the door. It was the blood of the lamb that turned away the wrath of God.
In whom we have redemption through his blood, the forgiveness of sins, according to the riches of his grace; (Ephesians 1:7 KJV)
But if we walk in the light, as he is in the light, we have fellowship one with another, and the blood of Jesus Christ his Son cleanseth us from all sin. (1 John 1:7 KJV)
You are reading into it and making up something that has no parallel. The blood was a sign.
Apparently, the all knowing God in this instance could not tell which household was Egyptian and which Hebrew, so He "needed" a visible marker!
For I will go through the land of Egypt on that night, and will strike down all the firstborn in the land of Egypt, both man and beast; and against all the gods of Egypt I will execute judgments—I am the LORD. [Ex 12:12]
"The blood shall be a sign for you on the houses where you live; and when I see the blood I will pass over you, and no plague will befall you to destroy you when I strike the land of Egypt. " [Ex 12:13]
Also, previous verses show that the lamb could be a goat! [Ex 12:5] The lamb did not atone for their sins; and no one was drinking its blood.
The lamb WAS sacrificed for the life of the inhabitants of that house
This "sacrifice" was not to atone for any sins.