Question for any resident Jewish posters about the lamb blood in Exodus

[Hindsight was 2020]

So being that it is both Passover and Easter is tomorrow I wanted to talk about an event in Exodus that is important in both faiths. When God decides in order to break Pharoh he sends the angle of death to take the first born sons of Egypt. To spare the Hebrews God tells Moses to tell the Hebrews to kill an innocent lamb and use its blood to mark their doors so that they would be spared by death. Now in Christian faith this event is supposed to be a foreshadowing of Jesus passion (ie the “lamb of god” who is “sacrificed” during Passover and by doing so saved us from death). So I was curious as to what the Jewish interpretation is about why God in particular said for innocent lamb blood to be the sign on the door.

[Statilius the Epicurean]

Not a Jewish theological response but it's probably an etiology for a customary feast day the Jews had.

Kinda related is that one of the most interesting archaeological discoveries we have is a letter from Jerusalem to local Jews in Egypt (where there was a temple) around the 5th century telling them how they're supposed to celebrate Passover, as if it's a newly innovated holiday.