What chakra corresponds to the lungs? Is it the heart or the throat chakra? I see the throat one corresponds to organs from the respiratory system so is this the correct one?
Both, but mostly the heart chakra. The heart chakra if it is blocked, it will make all of the muscles very tight in the chest and back, so they will not expand correctly to get a good breath.
Also consider the purpose of this 4th chakra is mostly as a connection between the top and bottom of the body and allowing energy to connect and flow between them. Which is similar to the lungs and heart breathing breath, life, and blood throughout the entire body.