The Holy God brought redemption and salvation to the Children of Israel. The blessings of the Holy God was bestowed upon them as they were brought out of Egypt. Sin must be made moral by the immortal sacrifice that can only be given of a wholly, Holy God. The connection is in the repetitive need for redemption because there is nothing Holy about a mortal animal. Between the blood on the lintel, and the Blood on the Cross was a multitude of sin.