Lots of time with lung shot deer, they bleed down into the chest cavity and what you are initially seeing on the trail beyond the hit site, is blood being aspirated from the nose and mouth. Once the chest cavity starts to fill with blood (doesnt take long), it begins pouring out of the exit wound or in the case with a broadhead, entrance and exit wounds, you'll start seeing it on both sides of the trail.
Killed a good 8 point a couple weeks ago. chunk of lung at the hit site about half the size of your thumb. No blood at all for the next 10-15 yds or so. At about the 15 yd mark, started leaking pretty good. At 30 yards it looked like a scene from axe murder, or chainsaw massacre, and he was laying in the middle of it all.
Similar with a 7 point my son got last week with a lung shot with entrance and exit about the same level mid-deer, first blood we found was 20 yards from the shot, then it was really spotty blood for another 20-30 yards until a dead deer. When we flipped him up onto the truck, started pouring out blood from the exit wound.
My son made the good point, that it may seem like the first blood was really far away from the point of the shot, but in truth the deer covered that ground in mere seconds. Really helps to pay attention after the shot and take landmarks where the deer runs, because you may not find blood for a while. Life experience tells me that you've got to look hard and long for a deer after you take a shot. It helps to have more eyes looking, too.