Lamb of God is a metaphor for the poor people who die in God's name(soldiers). There's is a Lamb of God christian/catholic chior.
The expression is used by Christian's to refer to Christ.
I'm not sure how much of the symbolism is intentional. The expression of a "lamb at the slaughter" refers to someone that is martyred, and also ritual sacrifice of animals was a part of pre-christian practice that was abolished in the new testament, so it is a fitting analogy.
But I think that it is more simply keeping with the pastoral metaphor employed by Christianity to refer to God or Jesus as the Shepard and to his worshipers as the flock. The lamb is chosen as being virtuous because it is white and timid and seen as pure, contrasted to the goat which is black and ill tempered. Not coincidentally, that is why the image of Satan is depicted showing aspects of Baphomet, a goat deity that was worshiped by the nomadic Canaanites, a rival group of the early Israelites (whom incurred God's wrath when they turned away from the worship of Him and embraced the former said deities of their neighbors).