In the multiplayer, dogs are lagging if you are too far from them. By far i mean 5-7 blocks.
Me and my friend are playing on a server, and we both observed this thing. If you are close to your dog, he will be normal, but if u will step back like 5 blocks he will start lagging.(one very short move in one second) If you will step back for aproximately 10 blocks, the dog will still lag but trying to reach you.(How dogs are supposed to do) I'm sorry for my english, i'm still learning it.