So, I have a geriatric male lab mix and a one(ish) year old male pit who just joined the family. The old lab has never been DA, and the pit, surprisingly, doesn't show any "normal" signs of being truly DA, either (yet, at least). On walks, the pit gets "happy butt" and "smiles" if he sees another dog and doesn't even bark back at chained/fenced dogs that bark at him/us.
My dogs have snarled and "air snapped" at each other a few times, tho. One time was the old dog apparently "telling" the puppy that no, he does NOT want to play and did not appreciate the puppy jumping on him playfully. Once (the more concerning time, IMO) it was the pit "puppy" trying to claim a scrap of food they both thought might be on the floor somewhere (there actually wasn't any food on the floor, but the half blind old dog thought there was and was sniffing for it. The pit saw what he was doing and started looking for it, too. And then out of nowhere (unless there were signals I missed) the pit was going "ARRrRawrRawr" and snarling and snapping at the old dog. It was really scary. Old dog just backed away, I yelled something like "OMG NO!!" at the pit, and put him outside. There was another time when both dogs snarled and snapped at each other, but I didn't see how it started.
An important point (I think?) is that neither dog actually touched the other in these encounters.
I've decided that for the rest of the old dog's life, I'm just going to be super-neurotic about food with them. I had tossed one treat to the new dog and another to the old dog when the pit kinda "went at" the old dog (and old dog found his treat, but thought maybe I'd thrown down more than one, hence his sniffing for a treat that wasn't there). I'm also supervising both dogs always when they're together, and making sure (to the best of my ability) that the puppy leaves the old dog alone. Old dog REALLY just wants the puppy to leave him alone.
So far, the situation seems to be de-escalating, which is good. The pit is fine with seeing old dog get treats out of my hand, and the old dog has moved to just going "ARF!!" when the pit puppy tries to play with him/falls on him/etc.
So far, I think we're doing ok, but any advice or insight would be appreciated.