As UriYosef said the paschal lamb blood in the first Passover was NOT for the remission of sins. It saved the PHYSICAL lives of the Jews who put it on their doorposts. It was an act of trust in G-d and defiance against the Egytians who worshipped lambs.

In subsequent Passovers the paschal lamb was a celebratory reminder -- and again had nothing whatsoever to do with sins.

Haven't we covered this all before, Mark?
And everything that Sarah tells you, listen to her voice. Genesis, 21:12