Regarding the question I would like to comment that not only in Catholic tradition the lamb represents Jesus.
In the old testament the Lamb was an animal offered in sacrifice to adorer God and to do a payment for the sins of people of God.
By the other hand, at the new Testament Jesus is the Perfect Lamb.
I think that the image of the Lamb above the priest's door symbolize the gentle nature of the priest in his interactions with the people.
