The USDA banned the sale of lungs for human consumption in 1971. I didn't know that until I just researched it. It's still legal to eat them, you just can't buy them. They can and are used in pet food. If you don't buy them they are legal. I will not comment on what I think of that ban but just mention the sale is banned. Do your own research as to why.
Sheep lungs are an essential ingredient in traditional Scottish Haggis. I've eaten traditional Scottish Haggis and lived. The Scots through the UK government regularly try to get the US ban lifted so the Scottish expatriots in the US can legally enjoy a traditional Scottish Haggis. Lung is eaten in many different cultures around the world from all kinds of animals.
Personally I remove the lungs when I butcher chickens and serve them back to the surviving flock. They don't go to waste. I part my chickens when I butcher so I have clear access to remove the lungs so I can't help you in how to remove them from a carcass. They don't always come out really cleanly, even with the body cavity opened. I use the backs for broth and if some bits of lung are left I don't worry about it. The percent of the overall product that is lung is pretty small and it's cooked really well when I make broth, especially if I pressure can it.