Almost slightly off-topic, but I'll comment with a real life story which took place near my home couple of months ago;
It was dark night, and one of my neighbours was driving home, about 80km/h speed on a quiet countryside road. Then, before he could react he saw sudden movement and the car went *THUMP* - being one of the local hunters with a lot of experience in identifying wildlife the driver could tell that it was a lynx crossing the road, got hit by the car. The driver thought it must have been an instant kill, or then the lynx was left suffering in the ditch next to the road. So he went to investigate. At that point I happened to pass by, stopped to see what is going on, and joined the search. We could not find a single hint of the lynx - surprisingly enough, it seemed that it didn't get injured that bad, and was able to retreat into the dark woods. So the neighbour alarmed the local hunting group.
After an hour the hunters had spread around, combing the forest looking for tracks. Also, a skilled dog was sent to track the lynx. After a while the hunters heard the alarm bark of the dog - and the sound was moving, so apparently the lynx was on the move and the dog was chasing it. Before the hunters could reach the location of the sounds they noticed that the sounds weren't moving. So maybe the lynx had collapsed because of injuries? The dog kept on barking, the hunters kept on approaching, and then suddenly they met the dog, who was fleeing in panic. The hunters followed the tracks for a while and found a place where the paw prints on the snow told a clear story; the lynx had been fighting with the dog, and the dog chose to flee - which seems like the most reasonable decision; the dog only has teeth, but the sharp claws of the fierce feline certainly are something to be afraid of.
The morale of the story; lynx are not to be messed with. It is realistic to assume that if a dog goes 1:1 fight with a lynx, the likely outcome is the dog either fleeing or getting seriously injured.
(I think the contemporary hunting dogs are trained to chase a lynx, hoping the lynx climbs a tree and stays there, so that the dog can keep it on hold and bark until the human companions arrive to relieve the situation.)