I would say you sliced him either high or low... My guess would be high if it took a while to find the blood. If you do not have any slick fatty tissue on the arrow or you just had Absolutely NO blood on the arrow? I would say its just a flesh wound and you sliced the skin on the deer somewhere.

My guess is he will live just fine...

I dont know of any animal lasting 30 seconds with a pass through lung hit.