It's my understanding that aerobic cellular respiration is summarized in the formula $C_6H_{12}O_6+O_2→CO_2+H_2O+ATP$ (unbalanced). The glucose is thrown through a series of chemical reactions, ultimately resulting in the binding of a phosphate group to ADP to form ATP to store energy, and the carbon dioxide is a byproduct of this process. At the very end of this chain, though, there's a few electrons left hanging, and the oxygen is used to bind these to loose protons to form water.
It is also my understanding that the primary purposes of the lungs are to intake $O_2$ and exhale $CO_2$ for this process and their role in speech.
Assuming this is all correct, are the secondary, minor functions of the lungs important enough that if there was a way to siphon the $e^-$ and $CO_2$ to some other function and find something else to allow the larynx to work we wouldn't need to breathe?