I can't imagine that a 1 lung hit deer can live. The lung is a primary organ w lots of blood flowing through it. Deer don't suffocate from being hit in the lungs, they bleed to death.
Good point. Deer do suffocate from being double lunged, because the pressure between the lung and chest wall (which is normally negative w.r.t. the atmosphere) drops to zero, and the lungs cannot inflate. However, since they typically goes down in a matter of seconds, massive blood loss appears to kill them before suffocation can.
As for the one lung case... I wasn't quite sure if the intrapleural space was separated between left and right, but it has to be. Otherwise the puncturing of one side would cause both lungs to collapse. This picture is the closest thing I could find to describe this. The lung on the left is unaffected even though the lung on the right is collapsed. The only way someone or something could survive this of course is if the bleeding stopped, which would only happen if very few blood vessels of the lung were cut. Also, breathing would be much more difficult obviously. If the deer was forced to run quickly for a long duration, the extreme oxygen debt could potentially kill it.